Composite materials fail generally by reaching a critical state, which culminates from a sequence of prior failure events. This paper is concerned with two specific early events, namely, the onset of matrix yielding and of fiber/matrix debonding. Continuing with an earlier work 1 (Elnekhaily and Talreja, 2018) that considered these failure events in a unidirectional polymer matrix composite with nonuniform fiber distribution subjected to transverse tension, the current work treats the case of combined axial shear and transverse tension. Using the same energy based criteria as before, the failure events are analyzed under different combinations of the two loading modes. While in the earlier work a two-dimensional representative area element was used based on a plane strain assumption, the current work uses a three-dimensional representative volume element. The results show the effects of the ratio of the axial shear to transverse tension on the two failure events. The variations of these effects with the fiber volume fraction and the degree of nonuniformity of fiber distribution are also illustrated.