The purpose of this work was to conduct mechanical tests for uniaxial compression of 3D core models manufactured using 3D printing using the photopolymer method—SLA. Based on the test results, the dependences of axial displacement on stress were obtained for each of the samples; it was found that at the initial moment of time the samples have high elasticity, the deformation increases slightly with increasing stress. Based on the test results, elastic moduli were determined for samples with different directions of printing layers. The influence of the orientation of the printing layers on the elastic properties of the samples has been established. The effect of internal strengthening of the material due to the peculiarities of layer-by-layer printing during ultraviolet curing of the photopolymer material has been revealed. The most elastic are samples with a vertical direction of the printing layers, the least elastic are those with a layer angle of 30°. The results obtained for printed models differ from the results obtained from the same kind of tests on rocks, which in turn confirms the need for this type of research to clarify the mechanisms of deformation of 3D models of rocks.