<p>The design of mat foundations is often done in structural analysis software using numerical models in which the soil is represented by linear elastic Winkler springs. Moreover, it has long been known that an accurate mat analysis requires a spatial distribution of spring stiffness constants under the mat that is highly non-uniform, with sharp peaks at the mat edges. However, due to large shear stress concentration close to the perimeter of the mat, in reality the soil there undergoes plastic yielding and loss of overall stiffness. This paper investigates the effects of soil nonlinearity and plastic yielding on the distribution of the stiffness of the equivalent linear Winker springs representing clayey soil under undrained conditions. For this purpose, series of parametric analyses of rectangular mat foundations resting on elastoplastic continuum were performed using the finite element code Abaqus. Two sets of analyses are conducted, one in which the soil is assumed to behave as linear elastic—perfectly plastic material and one accounting for pre-failure nonlinearity. The finite element analyses show that as the safety factor against bearing capacity failure decreases, the distribution of the back-calculated spring constants tends to become more uniform. Moreover, the results clearly demonstrate that modulus of subgrade reaction distributions that are often assumed in design practice are inadequate in properly capturing the mat-soil interaction, leading to significant errors in the calculation of the bending moments. Based on numerical results, sets of equations are developed for the estimation of the appropriate values of the spring constants across a mat as a function of the mobilized factor of safety. By taking into account the development of plastic deformation, the proposed equations permit the accurate determination of the mat bending for the full range of mobilized factor of safety, from zero loading up to bearing capacity failure.</p>