The present work has been conducted in order to develop a novel approach to predict the inhomogeneous flow of a 20MnCr5 steel during an axisymmetric hot compression test, by using the element-free Galerkin (EFG) method under a differential constitutive description. The governing equations have been solved on the basis of the EFG global weak formulation. A detailed explanation concerning the characteristics inherent to the application of the EFG method to this problem, has also been provided. Furthermore, a return mapping algorithm for the solution of associative von Mises inelastic problems, has been formulated for the differential constitutive description employed in this communication, namely, a differential return mapping algorithm (DRMA). The feasibility and suitability of the EFG method for solving the axial compression problem has been shown by comparing its results with a FEM based solution employing a simple constitutive description. The reliability of the proposed DRMA has been demonstrated by a comparison of a homogeneous deformation numerical test with the experimental and direct integration results reported in a previous communication. Finally, the EFG model has been used to predict the stress, strain and volume fraction recrystallized distributions under steady and transient nominal strain rate and temperature deformation conditions. These parametric studies have been carried out by considering the differential constitutive description, but also a conventional integrated constitutive model of a 20MnCr5 steel. The results have revealed the suitability of the EFG formulation under the proposed DRMA, for predicting the performance of an axisymmetric hot compression test. The differences between the use of differential and integrated constitutive descriptions on the performance of hot-working processes under inhomogeneous deformation conditions, have also been evidenced in this research work. •A differential constitutive description-based hot-compression model has been proposed.•The numerical solutions have been derived by means of the element-free Galerkin method.•A novel differential return mapping algorithm (DRMA) has been developed.•The DRMA was developed by computing the flow stress into an implicit difference scheme.•Notable differences were found with solutions based on integrated constitutive descriptions.