Elastic-plastic stress analysis of cracked fiber-reinforced plastic (FRP) was conducted by the finite element method. The inhomogeneous FRP was modeled as a two-dimensional laminated structure composed of elastic-perfectly plastic matrix material, orthotropic elastic fiber and homogeneous FRP. The size of the plastic zone near the tip of a mode II matrix crack was determined for an inhomogeneous composite and an unreinforced matrix material. Under the same value of the matrix stress intensity factor, KIIm the length and the height of the crack-tip plastic zone obtained for an inhomogeneous composite are equal to those obtained for an unreinforced matrix material in the range of KIIm≤0.2σY√(πdm) where σY is the yield stress of the matrix material and dm is the height of the matrix phase in the inhomogeneous FRP. On the other hand, for large KIIm value, the plastic zone length obtained for an inhomogeneous FRP is larger than that for an unreinforced matrix material, but the plastic zone height is smaller. A simple method is proposed to estimate the length and the height of the plastic zone ahead of the tip of a mode II crack from the elastic stress distribution in the inhomogeneous FRP.