Should  v.aux. (3rd sing. Should) past of *shall, used esp.: 1 in reported speech (i said i should be home soon). 2 a to express obligation or likelihood (i should tell you; you should have read it; they should have arrived by now). B to express a tentative suggestion (i should like to add). 3 a expressing the conditional mood in the 1st person (i should have been killed if i had gone). B forming a conditional clause (if you should see him).