In this work, an explicit integration scheme for hyperelastic-based finite strains elasto-plasticity is presented. One step update equations are obtained from the large deformation multiplicative elasto-plasticity theory, where an exponential variation of the plastic deformation gradient is assumed. In addition, the material tangent matrix is presented and has the same formal structure as the usual small strains elasto-plastic tangent matrix. In purely elastic regime, the proposal reduces to the usual large deformation elasticity equations. Routines to alleviate the main drawbacks of explicit methods are outlined, such as a yield surface drift correction scheme and an adaptive substepping method. Several examples of typical geotechnical tests using the Houlsby hyperelastic model along with the Modified Cam Clay plastic model are discussed. Results from a convergence test suggest that, using an adaptive substepping scheme, the error of the local problem is independent of the step size.