A dual particle method for problems in solid mechanics, on the basis of dual particle dynamics, is extended to applications of quasi-static deformations of solids. The general approach incorporates the discrete strong form of the governing equation, a Lagrangian representation of a moving least squares approximation of field variables and a spatial discretization comprised of two particle sets: motion points and stress points. The quasi-static dual particle method introduced in this work incorporates geometric and material nonlinearities as well as a modified method for applying traction boundary conditions. Some computational exercises are performed to verify the correct implementation of the method, show convergence behavior, and demonstrate the improved performance of the modified traction boundary condition application method. Copyright © 2012 John Wiley & Sons, Ltd.