For light mechanical structure, a hearing housing can no more be considered as rigid. The rolling Bearing rings are then elastically deformed under loading and loose their initial cylindrical shape. The load distribution among rolling elements is then modified which therefore changes the bearing life. A method is proposed to calculate the internal load distribution in a rolling bearing taking into account the housing elasticity. This allows one to estimate the Bearing life. This approach is useful to quantify the effect of the housing geometry - such as housing tolerance, width or thickness - on the Bearing life, A parametric study on the shape and dimensions of a groove machined on both side of the housing is presented, Finally the model is confronted with the experiment.