"must + [verb]" past simple

Question

Is there a way to use must in past simple?

Present simple: You must run.
Past perfect: You must have ran.

Past simple doesn't work: You must ran.
Not even with another word to indicate past (since must is ambiguous): I thought you must ran. (wrong)

Answer 1

had to

I must go. (present)

I had to go. (past)

Answer 2

Of the nine standard modal verbs in English, only eight of these are inflected for tense as four pairs:

Present Tense	Past Tense
will	would
shall	should
can	could
may	might

And these naturally pair like this:

Present Tense	Past Tense
Today, I think I will go.	Yesterday, I thought I would go.
I think I can get to it today.	I thought I could get to it yesterday.
It looks like it may rain today.	It looked like it might rain that night.

But the ninth modal, must, has no inflectional pair to use with either possible tense. It works best for a nonpast situation only:

Present Tense	Past Tense
Today I have decided that I must go shopping.	Yesterday I had decided that I must go shopping.
She must finish her project today.	—

And you cannot use must have either, because that is an epistemic use making a prediction of how the world is not a deontic use stating how the world needs to be but is not:

Present Tense	Past Tense
Surely she has gone home already.	Surely she had gone home already.
I think she must have gone home already.	I thought she must have gone home already.
I think she will have gone home already.	I thought she would have gone home already.

Therefore you must replace must with its periphrastic equivalent that employs a tensed auxiliary to carry the tense. Either to have to or to be to works fine for this:

Present Tense	Past Tense
She has to finish this today.	She had to finish that yesterday.
She is to finish this today.	She was to finish that yesterday.
I think she has to have gone home already.	I thought she had to have gone home already.
I think she will have to finish tomorrow.	I thought she would have to finish tomorrow.

When replacing must with one of those two periphrastic equivalents, the to be to version is more likely to be used epistemically for a prediction, while to have to is more apt to be used deontically for an obligation.

But this is not guaranteed. For example, these are all predictions not obligations:

• This must be John at the door now.
• This has to be John at the door now.
• That had to be John at the door back then.
• That must have been John at the door back then.
• That had to have been John at the door back then.