The main aim of this paper is to find if it is possible to identify material parameters using only three force-displacement dependencies, each for a different angle between the loading force and the principal material directions. The tested materials are textiles made of epoxy resin and fibers in the form of a glass plain weave, a glass quasi-unidirectional weave, a carbon plain weave, a carbon quasi-unidirectional weave, an aramid plain weave and an aramid quasi-unidirectional weave. The plain weave has theoretically 50 % of the fibers in the first and 50 % in the second principal material direction. The quasi-unidirectional weave has theoretically 90 % of the fibers in the first and 10 % in the second principal material direction. Seven types of specimens for each material were subjected to experimental tests. The first principal material direction of each material forms an angle between 0 ° and 90 ° with a step of 15 ° with the applied loading force. The results show that it is possible to identify the material parameters with sufficient accuracy using only three force-displacement dependencies for five out of six materials.