This paper presents the development of a cellular automaton taking into account the effects of neighborhood in the mechanical behavior of polycrystals. This model aims to have a better estimate of the elastic stress / strain field in polycrystals than conventional analytical models, such as the self-consistent model (SCM). As a first step in the consideration of neighborhood effects, the model was developed in the case of a uniaxial loading in linear elasticity. A Kelvin structure is used to represent the polycrystal in order to negate any grain size and shape effect, in order to focus primarily on the influence of crystallographic orientations. The model has been developed based on the hypotheses from a Finite Element Method (FEM) study of the influence of a grain’s neighborhood on its behavior. FEM, SCM and the analytical model here presented are finally compared grain by grain after a simulation on polycrystalline aggregates of 686 grains using the Kelvin structure. Taking the FEM results as a reference, the results of our model show an approximation almost three times better than those of the SCM which show the importance of taking into account the neighborhood effect.