The present work has been conducted to develop a straightforward procedure for solving the thermal–mechanical problem in a conventional continuous casting (CC) process using the element free Galerkin method. The linear momentum balance equation has been developed on the basis of this global weak formulation. The model has been solved under a nodes-fixed mixed Eulerian–Lagrangian description to estimate the mechanical behavior of a round billet during the CC process in the mold region. The proposed approach is developed in a predictor–corrector scheme, which provides a solution involving simultaneously all the materials configuration downwards the mold without the requirement of a viscoplastic tangent operator. The results have revealed that this technique could be used successfully in the modeling of continuous casting thermal–mechanical problems