to lie (down) on your belly / to lie (down) on your back
lie/layで迷うことが多いとは思うのですが、lie で「横になって（休む）」という意味があります。
lay は、何かを「置く」時に使われます。
I lie on my back at the end of a yoga session.
We lay flower every morning.
文学的・詩的な表現で、lay me down という言い方もありますよ。
（Simon & Garfunkel の曲（明日にかける橋）で、"I will lay me down" とあるように）
"My husband always snores terribly. I try to wake him up but he is always in such a deep sleep, that's impossible. What can I do?"
"Does your husband sleep lying face down?"
"No, he always sleeps lying on his back. Sometimes I pinch his nose and he stops snoring for a while, but he soon starts snoring again!"
【例文】
"My husband always snores terribly. I try to wake him up but he is always in such a deep sleep, that's impossible. What can I do?"
（私の夫はいつもひどいいびきをかきます。起こそうとしますが、いつも深い眠りについていて起こせません。どうしたらよいでしょうか？）
"Does your husband sleep lying face down?"
（あなたの夫はうつ伏せで寝ていますか？）
"No, he always sleeps lying on his back. Sometimes I pinch his nose and he stops snoring for a while, but he soon starts snoring again!"
（いいえ、いつも仰向けで寝ています。時々私は彼の鼻をつまむといびきがしばらく止みますが、すぐにまたいびきをかき始めます！）
"Sleeping face up" or " Sleeping on my back" expresses you sleeping on your back looking up at the roof.
I like sleeping on my back/ I prefer sleeping face up.
"Face down" or "Sleeping on my stomach" expresses your stomach/front of your body is on the mattress.
I like sleeping face down/ I prefer sleeping on my stomach.
"Sleeping face up"（顔を上向きにして寝る）又は " Sleeping on my back"（仰向けで寝る）は仰向けで屋根を見て寝ることを表しています。
例文
I like sleeping on my back/ I prefer sleeping face up.
仰向けで寝るのが好きだ/顔を上向きにして寝るほうが好きだ
"Face down" （顔を下にして）又は "Sleeping on my stomach"（うつ伏せで寝る）はお腹/体の中心をマットレスの上にしているということです。
例文
I like sleeping face down/ I prefer sleeping on my stomach.
顔を下にして寝るのが好きだ/うつ伏せで寝るのが好きだ
How one lays down when sleeping or undergoing some kind of medical procedure is usually described. For instance a surgeon might tell a patient prior to his undergoing anesthesia: Mr. Jones, please lay down on your back and look at me. It seems that there is no difference in either japanese or English as to how this concept is explained.
Please note: the verbal expression Face up means to confront or to deal with and has no relation to one's position.
The belly is the front part of the human trunk below the ribs, containing the stomach and bowels. However, despite the fact that the stomach is just one of the internal organs of the body, people still often refer to the front part of the body below the chest as the stomach. So, its not unusual for someone to say:
He was fast asleep, lying on his stomach.
However, it would be appropriate to say:
I found him lying on his belly.
The noun 'belly' has several meanings, but, in this context, it means the front part of the human trunk below the ribs, containing the stomach and bowels. So, you can see, the stomach is in the belly.
If you found someone lying down, facing up, you may say:
I found him lying on his back.
The bellyはお腹のことです。 stomachは内臓ですがお腹のことを指すときがあります。このように使うことがあります :
（英文） He was fast asleep, lying on his stomach.
（訳）彼はうつ伏せになって寝ていた。
このようにも使えます:
（英文）I found him lying on his belly.
（訳）私は彼がうつ伏せになって寝ているところを見た。
名詞の 'belly' はいろんな意味がありますが一般的にはお腹のことをさしています。the stomachはbellyの中にあります。
うつ伏せになって寝ている人を見つけた場合このフレーズを使えます:
I found him lying on his back.
We are all in the prone position when we sleep!
We are said to be... "Lying Down, or " reclining;-)
However the other options are:
'Sleeping on your side..."
"Sleeping Face up"
or sleeping "Face down"
Some people are said to be "tossing and turning all night;-)) never settling!
"I sleep on my back" ...is also a way to describe the face up position.
寝るときはだれでも横になりますね！
その体勢を lying down または reclining といいます。
しかし他にも言い方があります。
Sleeping on your side...
（横になって寝る）
Sleeping face up
（仰向けになって寝る）
Sleeping face down
（うつ伏せになって寝る）
人によってはじっと寝ないで
tossing and turning all night （ゴロゴロと寝返りをうつ）
という感じで寝る人もいます。
I sleep on my back
これも「仰向けで寝る」という意味です。
Face down - To sleep facing down this would mean sleeping with your face and belly down.
Laying on your back - This is where you will sleep with your face and belly up.
Face down - "To sleep facing down" で「うつぶせに寝る」という意味になります。
Lying on your back - これは「あおむけに寝る」という意味です。
If you sleep on your belly you can say, "I sleep face down"
If you sleep face up you can say, "I sleep face up" or "I sleep back down"
Saying, "I sleep face down" is a casual way of saying you sleep on your stomach. While when you say, "I sleep face up" you indicating that you are laying in a position where your face is literally facing up to the ceiling.
"I sleep face down"ということはカジュアルな表現でうつぶせに寝るという意味になります。
おまけに "I sleep face up"という時は 文字通り天井に顔を向けて仰向けに寝るという意味になります。
"sleeping on your back"
To lay on your back often described as face up, as your face is facing upward.
"sleeping on your front"
This term is used when you are sleeping/laying on your front, also known as face down, as your face is facing down, laying on your stomach.
"sleeping on your back"（あおむけに寝る）
あおむけに寝ることはしばしば 'face up' と表されます。顔が上の向いているからです。
"sleeping on your front"（うつぶせに寝る）
これはうつぶせに寝るの意味です。'face down' ともいいます。顔が下を向いているからです。
face upは「顔を上にして」、つまり、「仰向けで」という意味
face downは「顔を下にして」、つまり、「うつ伏せで」という意味です。
He is sleeping face down.
「彼はうつ伏せで眠っている」
He is sleeping face up.
「彼は仰向けで眠っている」
以上です。
少しでも参考になれば幸いです(*^_^*)
日本 
イギリス 
南アフリカ 
アメリカ合衆国 
