Quasi-ideals in a semiring are the generalization of one-sided right ideals and left ideals. Biideals are generalized form of the quasi-ideals. This paper is concerned with these two types of ideals in the semirings from pure algebraic point of view. We shall characterize three important classes of semirings namely regular semirings, intra-regular semirings and weakly regular semirings by the characteristics of their quasi and bi-ideals along with their right and left-ideals. having no negative elements were initially defined