The prediction of fatigue in materials and structures is usually based on experimental Wohler curves, relating the number of cycles to failure to the amplitude of the applied cyclic loading. Those curves show some scattering due notably to the variability of the microstructure. Predicting fatigue lifetime can thus be seen as a statistical problem that depends on microstructural descriptors. This paper paves the way to a probabilistic approach for quantitatively linking crystallographic and morphological texture data to fatigue lifetime prediction. In more detail, a simplified mesoscopic model is constructed for calculating the evolution of an elastic-plastic polycrystal with a prescribed texture. That model is limited to high cycle fatigue, corresponding to cyclic loadings of sufficiently low amplitude for plasticity to be mainly confined to few well-separated grains. The model obtained takes details of the texture into account, i.e. the distribution, shape and orientation of the individual grains. It relies on analytical formula and is mesh-free. A comparison with full-field finite element simulation shows that the proposed model leads to satisfactory results in regard to its complexity. In the case of cyclic loading, we show that the model presented leads to a direct method for calculating the asymptotic values of the plastic slips (and cumulated plastic slips) reached in each grain when the number of cycles grows to infinity. We show how that direct approach can be used for upscaling a local failure criterion to the mesoscopic scale and performing probabilistic analysis.