We investigate a minimal model of the plastic deformation of a material with random microstructure. The material elements are assumed to exhibit ideally plastic behavior (J2 plasticity). Structural disorder is introduced in terms of random variations of the local yield stresses. Using a finite element implementation of this simple model, we simulate the plane-strain deformation of specimen loaded in tension. The resulting strain patterns are statistically characterized in terms of their spatial correlation functions. We furthermore study the corresponding surface morphology in terms of long range correlations in the deformation patterns.