It is a well known fact that polycrystals exhibit grain size dependence. Traditional continuum models can however not catch this effect. Lately, there has however been an increased interest in the development of non-local theories that can account for the size effect. In this work a non-local crystal plasticity theory is implemented, where slip gradients enter in the hardening modulus. A new proposal for the incorporation of strain gradients in the hardening modulus is presented. The non-local theory is used in a three-dimensional finite element model to model Aluminum (Al). A representative volume element (RVE) containing a random grain structure is used to model the material by the finite element method (FEM). Thus, the mesh is partitioned into a periodic grain structure by a discrete version of the Voronoi algorithm. The model is used to simulate uniaxial tension, by using periodic boundary conditions to constrain the model. The non-local theory contains an internal length scale I that needs to be defined in the model. The internal length scale is determined from comparisons to reported experimental data on Al. The coupling between the microstructure and the numerical model is discussed, and the proposed hardening relation is justified. It is shown that a model containing 30 grains predicts the grain size effect well. But cells containing 15, 45 and 60 grains are also investigated. It is shown that the size effect can be predicted by changing the size of the periodic cell, and also by changing the number of grains in the cell.