Paper presents results of the modelling of the magnetic B(H) characteristics of amorphous magnetic materials with the following compositions in the as-quenched state: Co68Fe4B13.5Mo1.5, Fe78Si13B9, Fe40Ni38Mo4B18 and Fe73.5Nb3Cu1Si13.5B9. On the base of experimental B(H) characteristics values of Jiles-Atherton-Sablik model's parameters were calculated. For this calculation evolutional strategies together with gradient Hook-Jevis optimisation were applied. Presented results indicates the good agreement between experimental results and Jiles-Atherton-Sablik model. As a result this model can be utilized for modelling of magnetic characteristics of the soft amorphous magnetic materials for sensor applications as well as for quantitative determination of physical material parameters (such as anisotropy energy density) on the base of the magnetic hysteresis loop.