The discrete element method is a method for simulation of a particle system. For the "soft-sphere" mechanism of particle interactions, there are several models for normal contact forces, namely linear spring-dashpot, and non-linear damped Hertzian spring-dashpot, among others. The focus of this paper is to determine the normal spring stiffness coefficient of the linear model through the numerical solution for the overlap between particles in non-linear models. The linear spring stiffness is determined using equivalence between the linear and the nonlinear models. Using the MFIX computational code, the proposed approach is applied in the numerical simulations of two problems: single freely falling particle and bubbling fluidized bed. A method based on mean dimensionless overlap is suggested as an initial estimate to determine the normal spring stiffness coefficient. Other possible methods for computing the stiffness coefficient are also discussed in this work, e.g., maximum dimensionless overlap and dimensionless contact duration. (C) 2013 Elsevier B.V. All rights reserved.