Add to ORKG© Published under licence by IOP Publishing Ltd. The work is concerned with development of algorithm for numerical investigation of stress-strain state of elastic solids, taking into account the incompressibility of materials. The kinematics of continua is described in terms of the deformation gradient tensor and left Cauchy-Green tensor. The stress state is described by the Cauchy stress tensor. Constitutive equations are received using a potential energy of deformation. An incremental method is used to solve the nonlinear problems. The penalty method is applied for a modelling of the incompressibility of the material. Numerical realization is based on a finite element method