Additive manufacturing is being increasingly used both for rapid prototyping as well as the fabrication of finished components. It is important to determine how the properties of 3D printed materials change over time and how they affect the durability and usability of products. The aim of the research presented in this article was to find out what influence the natural aging period had on the mechanical properties, especially the tensile strength and modulus of elasticity, of specimens made from the selected photocurable resins using the PolyJet Matrix (PJM) technology. The tests involved determining the tensile strength and modulus of elasticity of specimens fabricated in 2013 and 2014 using two types of photosensitive resins, i.e., FullCure 720 and VeroWhite, respectively. Some of the specimens were stored under laboratory conditions until July 2022 and then tested using a universal testing machine. The experimental data obtained in 2022 for the naturally aged models were compared with those reported for the as-printed specimens. One of the main findings of this study was that the tensile strength and modulus of elasticity of the naturally aged specimens were largely dependent on the printing direction (model orientation on the build tray). The test results show that aging generally decreased the tensile strength of the specimens. In one case, however, an increase in this property was observed. For the X and Y printing directions, Rm declined by 27.1% and 30.7%, respectively. For the Z direction, a decrease of only 5.5% was reported, for Full Cure 720. The modulus of elasticity of the models tested in 2022 differed considerably from that reported for the as-printed objects. Higher values of the modulus of elasticity implied that the material stiffness increased over time, and this is a common phenomenon in polymers. Interesting results were obtained for VeroWhite specimens. The modulus of elasticity decreased significantly by 25.1% and 42.4% for the specimens printed in the X and Z directions, respectively. However, for the models built in the Y direction, it increased by 27.4%. The experimental data may be of significance to users of products manufactured using the PJM method as well as to researchers dealing with the durability and reliability of such materials.