It is critical to handle geometric and material nonlinearities in a stable manner while solving the problems from solid mechanics, such that it results in a converged solution. The present work compares the suitability of generalised displacement control (GDC) and displacement control algorithms (DCA) by solving several 1D and 2D formulations. The ability of these algorithms to handle homogeneous and inhomogeneous deformations is also studied. A novel direct displacement control method (DDCM), coupled with Newton-Raphson method, is proposed and compared with GDC and DCA approaches. Appropriate conclusions are finally drawn based on the successful demonstrations of the numerical results obtained by GDC, DCA and DDCM approaches. Copyright © 2019 Inderscience Enterprises Ltd.