Three-dimensional printing is finding increasing applications in today’s world. Due to the accuracy and the possibility of rapid production, the CAD/CAM (computer-aided design/computer-aided manufacturing) technology has become the most desired approach in the preparation of elements, especially in medicine and dentistry. This study aimed to compare the biomechanical properties, fractal dimension (FD), and texture of three selected materials used for 3D printing in dentistry. Three biomaterials used in 3D printing were evaluated. The materials were subjected to the compression test. Then, their mechanical features, FD, and texture were analyzed. All the tested materials showed different values for the studied properties. The only statistically insignificant difference was observed for the force used in the compression test. All three materials showed differences in width and height measurements. The difference in the decrease between the compression plates was also significant. For Dental LT Clear, the mean value was 0.098 mm (SD = 0.010), while for BioMed Amber it was 0.059 mm (SD = 0.019), and for IBT it was 0.356 mm (SD = 0.015). The nominal strain also differed between the materials. IBT had the highest mean value (7.98), while BioMed Amber had the smallest (1.31). FD analysis revealed that Dental LT Clear did not show differences in the structure of the material. The other two materials showed significant changes after the compression test. Texture analysis (TA) revealed similar results: BioMed Amber resin showed significantly less pronounced texture changes compared to the other two materials. BioMed Amber also showed the most stable mechanical properties, whereas those of IBT changed the most. Fractal analysis revealed that IBT showed significant differences from the other two materials, whereas TA showed that only Dental LT Clear did not show changes in its texture after the compression test. Before the compression, however, BioMed Amber differed the most when bone index was taken into account.