Using the spectroscopic analysis and the theoretical modeling, physical properties of the nearby astrometric binary $\mu$ Cas have been determined. In spite of the well-defined parallax and astrometric orbit, there has been a chronic mass ratio problem between components. Recently, the radius of the primary component has been detected from the optical interferometric observation of the CHARA array. Using the high resolution spectroscopic analysis, we found that $\mu$ Cas have $\alpha$-enhanced chemical composition with respect to the scaled solar abundance by a factor of two. Combining our abundance analysis with recently determined physical properties, the consistent models for $\mu$ Cas have been constructed within the frame work of standard stellar theory. Through a statistical minimization between theoretical model grids, a reliable set of physical dimensions has been defined. Furthermore, the mode oscillation frequency of the best model has been calculated.