Should ( 2 )

You can use should after a number of verbs, especially:

suggest  propose  recommend  insist  demand

They insisted that we should have dinner with them.

I demanded that he should apologise.

What do you suggest I should do?

In the same way, you can use should after suggestion / proposal / recommendation etc.:

What do you think of Jane’s suggestion that I should buy a car?

and also after ‘it’s important / vital / necessary / essential that…’:

It’s essential that you should be here on time.

Sometimes you can leave out should:

It’s essential that you be here on time. ( = that you should be here )

You can use normal present and past tenses:

It’s essential that you are here on time.

I demanded that he apologised.

You can use should after a number of adjectives, especially:

strange  odd  funny  typical  natural  interesting  surprised  surprising

It’s strange that he should be late. He’s usually on time.

I was surprised that she should say such a thing.

If…should…

You can say ‘if something should happen…’. For example:

If  Tom should phone while I’m out, tell him I will phone him back later.

‘If Tom should phone’ is similar to ‘If Tom phones”. With should ,the speaker feels that the possibility is smaller.

You can also put should at the beginning of the sentence:

Should Tom phone, can you tell him I’ll phone him back later?

You can use I should… / I shouldn’t… to give somebody advice. For example:

Shall I live now? No, I should wait a bit longer.

Here ‘I should wait’ = ‘I would wait if I were you, I advise you to wait’.