This paper presents a means of reducing the computational cost of finite element (FE) simulations coupled to polycrystal plasticity theory. One typically assumes that a polycrystal with a large number of grains underlies every integration point of the FE mesh. Instead, it is suggested here using reduced samplings of grains which differ from one integration point to another. On average, every set of 5 to 25 finite elements contains a variety of lattice orientations that is representative of the macroscopic texture. The model is applied to deep-drawing of a cylindrical cup made of steel. In a first set of simulations, grains are assigned orientations representative of a cold rolling texture and the "earing" profile is compared to experiment. In a second set of simulations, lattice orientations are random and an isotropic deep-drawing result is expected. It is demonstrated that using a minimum of 20 grains per integration point allows properly predicting the final shape of the cup and the texture development.