Samples of porous NiTi were obtained by the method of self-propagating high-temperature synthesis. The mechanical characteristics of the porous ones were studied by quasi-static compression. When the samples of porous titanium nickelide were subject to quasi-static compression, the deformation was of an elastic-plastic nature. Three characteristic types of the fracture surface under quasi-static compression of the porous SHS -TiNi alloy were identified: 1) ductile fracture of the austenite phase in the form of a cup relief, 2) brittle fracture accompanied by the formation of cleavage steps, 3) large areas of plastic shear deformation, on which cups and cleavage facets were nucleated. To determine the anisotropy of the porous TiNi alloy properties, the volume of the porous sample was simulated, and estimated calculations were carried out. Based on the results of reconstructing 3D neutron high resolution tomography of the porous volume of titanium nickelide and the numerical parameters of the model porous medium, an algorithm was developed for obtaining a solid-state 3D model of the porous framework for using in finite element calculations. The studied porous titanium nickelide alloy, as well as spongy bone tissues, was shown to have orthotropic elastic properties conditioned by the geometric features of the porous framework. The effective moduli of elasticity and shear for the porous volume of the material were determined. The calculation results of the elastic moduli for the studied model of porous titanium nickelide numerically agree with the results obtained by compressing the samples of porous TiNi. The porous TiNi alloy under uniaxial compression was established to be destroyed under the action of tangential shear stresses at an angle of 45 degrees to the direction of uniaxial compression.