This paper aims to give a preliminary proposal to DRT to represent the universal and existential readings of donkey sentences within the framework of Kamp and Reyle (1993). When only EVERY DRS construction rule is applied to donkey sentences without any universal effect, existential readings as basic and universal readings as additional can be obtained from them. Meanwhile, whenever universal effect comes out of the context, UNIVERSAL EFFECT DRS construction rule I propose in this paper should be applied to the donkey pronoun. The result is that only universal readings will be obtained. Though some donkey sentences have only existential readings and others only universal readings, the typical donkey sentences are ambiguous for two readings. In this respect, along with Chierchia (1995), I presume that existential readings are basic and universal readings are additional. I try to seek an adequate proposal in this paper, on the basis that universal readings are stronger, in the sense that they entail the corresponding existential readings.