AbstractA two parameter family of incrementally objective integration schemes is proposed for the analysis of a broad range of unified rate‐dependent viscoplastic constitutive models in large deformation problems. A similar scheme can be applied to rate‐independent solids as well. These algorithms are a generalization of the mid‐point integration rule. Full linearization of the principle of virtual work is performed in an updated Lagrangian framework together with a calculation of the consistent linearized moduli. Some details of the finite element implementation are given for plane strain and axisymmetric problems. The method is compared with other objective integration schemes and is tested with several examples where large strains and rotations