A stent is a mesh that is placed in a narrowed or closed part of a blood vessel. They play a crucial role in the treatment of various cardiovascular diseases by providing mechanical support to arteries and facilitating blood flow. The mechanical properties of vascular stents, such as radial strength, flexibility, and conformability, are critical for successful deployment and stability within the arterial environment. Thus optimal design of these medical devices is very important. In this study, we address a series of optimal design problems with parameters related to stent strut thickness and the geometry of struts. The optimization algorithm is of the gradient type and efficient since it is grounded on the elastic stent model with struts modeled by the one-dimensional curved rod model. This research contributes to advancing the precision and efficacy of cardiovascular interventions by refining the design parameters critical to stent performance.