The paper presents a new idea of extension of the Jiles-Atherton-Sablik model for modeling of the influence of mechanical stresses on magnetic hysteresis loops of amorphous alloys. In the extended model changes of parameter k are considered during the magnetization and the influence of stresses on eight parameters of the Jiles-Atherton-Sablik model is taken into account. Verification of the model was carried out on the base of experimental results obtained for Fe40Ni38Mo4B18 amorphous alloy subjected to both stress from external compressive force as well as shearing stresses from torque. In the experiment uniform stress distribution was achieved in both cases due to special mechanical system of backings. Evolutionary strategies were used in conjunction with gradient optimization for calculation of the model parameters. Results of simulation are in good agreement with experimental findings. As a result the extended Jiles- Atherton-Sablik model enables modeling of the magnetoelastic characteristics of amorphous materials for mechatronic inductive components such as compressive stress and torque sensors.