Hi Lee, "She should arrive by now." (You are expecting her to arrive anytime as you speak. Besides being used to express responsibilities and obligations, "should" also expresses expectation.) "She should have arrived by now." (You are expecting her to have arrived some time ago due to the use of present perfect tense (have arrived), yet you don't see her.)

Hey Lee YC, how are you? The first sentence is not correct; whereas the second one is. ''She should have arrived by now'' means either that you expect her to have arrived already or that she was expected to have arrived, but still haven't. May I provide you with an explanation on the usage of ''should + have'' construction, for a better understanding: --> You use ''should'' or ''ought to'' with ''have'' and an ''-ed participle'' to say that you expect something to have happened already. E.g.: ''You should have heard by now that I'm O.K.'' E.g.: ''It's ten o'clock, so they ought to have reached the station.'' --> You also use ''should'' or ''ought to'' with ''have'' and an ''-ed participle'' to say that something was expected to happen, but did not happen. E.g.: ''The letters, which should have been sent to that address, were forwarded to another.'' E.g.: ''The project ought to have finished by now.'' *Be Careful! You must use ''have'' and an ''-ed participle'' in sentences like these. Don't say, for example, 'The project ought to finish by now'. Likewise, you must not say 'She should arrive by now', as in the first example you provided. Hope that helps!!! Should you have any further questions/doubts regarding English grammar, do not hesitate to contact me. I shall be pleased to help.

It is better to say "she should have arrived by now". You wouldn't say "she should arrive by now"

she should arrive by now. she should have arrived by now. It is better to use the second sentence. That means you were expecting her to arrive at a certain time and she has not shown up yet.

Both sentences are grammatically correct but they differ in meaning. "She should arrive by now", implies that you are sure and confident that the person you are waiting for will arrive at that time. "She should have arrived by now," on the otherhand can either express worry or assurance. It depends on how it is used on the context. It expresses worry since the person you expected to arrive at that particular time have not yet arrived. It could also express assurance, for example: A mother is worrying for her daughter since it was her daughter's first time to go abroad alone. The father assures the wife with a smile and says, "She's fine. She should have arrived by now."