The original is wrong but you don't have to change it to "They were supposed to ...".
They should have finished their task last week.

Student or Learner
Dear teachers,
If a modal verb doesn't have a past tense, can we use it in past tense sentences?
Like :
They should finish their task last week.(This sentence is wrong, right?)
We should say:"They were supposed to finish their task last week", right?
So does that mean if a modal verb doesn't have a past tense, we can't use them in past tense sentences?
Thanks a lot!
The original is wrong but you don't have to change it to "They were supposed to ...".
They should have finished their task last week.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
Modal verbs can have a past aspect (if that's the correct word) in sentences like this: They were told last year that they should finish the job. You could replace should in that sentence with "had to".
I am not a teacher.
But the sentence:
"They should have finished their task last week" means "They didn't finish their task last week" or it means you are guessing that they finished their task last week right?
If I want to say they were required to finish the task last week.
How can I say?
No. It's wrong, as ems told you in post #2.
It means they didn't finish the task last week as they were supposed to have done.
Here's a corrected version of your text:
But, does the sentence "They should have finished their task last week" mean they didn't finish their task last week, or does it mean you are guessing that they did finish their task?
This is supposing that I want to say they were required to finish the task last week.
How can I say this?
I am not a teacher.
Technically, could, might, shall and would are the past-tense forms of can, may, shall and wiil respectively, though they are not often used as past-time forms Two of these can be used as past-time forms in some contexts.
I can play the piano. I could play the piano when I was only five.
Luke will spend hours on his computer. Luke would spend hours on his computer when he was younger.
All can be used as backshifted forms in reported speech.
"I can/may/will see you tomorrow"
Lindsay said she could/might/would see me the following day.
"Shall I close the window?"
Peter asked if he should close the window.
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