Summary: This paper deals with a new mixed algorithm based on the Inverse Approach named “Pseudo Inverse Approach”. It has been developed to take into account the deformation history: some realistic configurations are introduced to calculate the strain increments between two successive configurations. These configurations are generated by a geometrical based procedure. The total strain between the initial configuration and an intermediate configuration can be determined by the Inverse Approach. Then the strain increment between two successive configurations is obtained in order to make the stress plastic integration based on the flow theory of plasticity.