The present paper describes a parametric design and optimization tool [Support Optimization and Design Tool (SODT)], used to evaluate passive axial support positions on circular solid meniscus mirrors. The developed tool avoids the intrinsic limitations of methodologies of the reference literature, based on analytical formulations. A parametric finite element model of the mirror is generated from the user inputs and the support distribution is optimized in terms of the root mean square of the surface error (SFE). The optimization process is based on a hybrid optimization algorithm combining genetic algorithms and a gradient-based approach. The results are compared to the ones presented in the literature, evidencing minor discrepancies that can be basically attributed to differences in methodology and structural formulation, as it is discussed in the text. Finally, the finite element and optical postprocessing results are verified against industry-grade software: MSC Nastran^® and Sigmadyne SigFit^®.