be supposed to do有三种意思：1 表示责任、义务或权威人士要求做的事，可用should替换；2 表示人们期待某件事以特定方式发生或产生特定结果，也可以用should替代；3 被人们普遍认为具有某种性质或技能。可被be thought to do/to be替代。

因此，be supposed to do可以用来表示推测、义务。

如果是表示对过去的推测，不定式用完成体。例如：

He is supposed to have arrived. 他可能已经到了。=He should have arrived by now.

表示本该做某事，而实际未做，属于虚拟语气表示与事实相反的用法。这种虚拟语气谓语中的限定动词必须是某个动词的过去形式，不可能是现在式。通常用should have done.

如果用be supposed to do，be不能用现在形式，因为现在已经知道事实不是如此，人们现在已经不再假设如何如何了。必须使用过去式的be.（should have done之所以能表示本该做某事而实际未做，与should是shall的过去式形式有关。）

You should have finished your homework by Sunday.

You were supposed to have finished your homework by Sunday.

以上二句意思相同：本该周日前完成作业，而实际未完成。

如果用are，则为推测用法。

You are supposed to have finished your homework by Sunday.你可能在周日前把作业都写完了吧。

请注意《麦克米伦英语词典》以下例句：

Today was supposed to have been sunny, but it’s raining.

注意句子的两个限定动词形式。

The train is supposed to have arrived an hour ago.

大约等于：The train is thought to have arrived an hour ago.或者It is likely that the train arrived an hour ago.

这句话中限定动词为现在形式is，只能是推测性用法，意为：火车可能在一小时前已经到了吧。

The train was supposed to arrive an hour ago

这句话仅仅表示过去的期待：火车应该在一小时前到达。（具体是否到达不知道。也未做推测。）

如果将不定式改为完成体，则意义不同：

The train was srpposed to have arrived an hour ago.

火车本该一小时前到达，但实际没有到。

be supposed to 的用法可以归纳如下
 【1】 be supposed to... 其中to是动词不定式符号，不是介词，其后要跟动词原形。当be supposed to... 的主语是“人” 时，意为“应该…… ”；“被期望……”，它可以用来表示劝告、建议、义务、责任等，相当于情态动词should。

 Everyone is supposed to wear a seat-belt in the car.

 每个人在汽车里都应该系安全带。
Teachers are supposed to treat all the students alike.

老师应该对所有的学生一视同仁。 
 【2】当be supposed to... 的主语是“物”时，它表示“本应；本该”，用于表示“某事本应该发生而没有发生”
The new laws are supposed to prevent crime.

这些新法令本应该起到防止犯罪的作用。
The train was supposed to arrive half an hour ago.

火车本应在半小时之前到达。
 【3】 be supposed to后面接“have + 过去分词”时，表示“本应该做某事而没做”。

  You are supposed to have handed in your homework by now.

现在你应该已经把作业交上来了。
He is supposed to have arrived an hour ago.

他应该一小时前就到了。
【4】 be supposed to... 的否定结构为be not supposedto...,它常用于口语中，意为“不被许可；不应当”。
 She was not supposed to be angry about that.

她本不该为那件事而生气的。
You are not supposed to smoke on the bus.

你不应该在公共汽车上吸烟。