Mars habitation is a highly challenging engineering problem due to its extreme environmental conditions, which make human habitation difficult. The Martian atmosphere is extremely thin, with a surface pressure of approximately 600 pascals, and the surface temperature stays very low, around 211 kelvins. The solar radiation keeps fluctuating, and dust storms create wind-driven surface flows. These conditions impose major design restrictions, which require structures to endure high pressure differentials, extreme cold weather and strong wind conditions. Therefore, it is necessary to address these coupled challenges through an integrated design strategy in the early stages of Mars surface habitat development. This work performs a complete numerical analysis using a multiphysics approach to study a theoretical Mars sub-surface habitat system. Two habitat geometries, cylindrical and hemispherical, are modeled using CAD and analyzed using commercial finite element and computational fluid dynamics tools. The structural performance analysis assesses internal pressurization, which meets human-rated conditions. Thermal behavior is analyzed using steady-state heat transfer analysis of a multilayer wall system comprising an aluminum structural shell, a regolith layer, and a low-conductivity insulation layer. The study includes solar radiation effects through solar flux analysis, which considers four representative Martian years (MY48-MY51). Aerodynamic analysis is also performed to evaluate the habitat stability under Mars wind loading. The results demonstrate that habitat geometry and multilayer wall design significantly affect performance. The hemispherical design decreases structural deformation by more than ten times when compared to cylindrical geometries. The thermal analysis demonstrates insulation effectiveness, which results in 80-90% less conductive heat transfer, while regolith provides extra thermal insulation. The aerodynamic results demonstrate that the curved habitat remains stable when exposed to wind forces. The results create a practical base for initial Mars habitat development, which will later include radiation and dust assessment.