Glancing the literature, semicircular, arc and skewed angular data is observed in the applications such as Feldspar laths data (Fisher, 1993, p. 240), Face - cleat in a coal seam data (Fisher, 1993, p. 254), Fallen trees data (Toshihiro, et al., 2012), face recognition problem, etc., and not much was done to model such angular data. Moreover Chi – Square distribution can be used as a quick test of significance in most situations, especially using machine learning algorithms. This finer pointer has become a motivating factor to work on l - axial (arc) models, and they can be viewed as the most general angular models from which Circular, Semicircular and other kinds of models could be deduced as particular cases and also to derive new angular model from Chi-Square distribution. In this paper, the authors introduce a new semicircular model, induced by Modified Inverse Stereographic Projection on Chi-Square distribution for modeling semicircular data. The authors extend it to the l- axial Chi-Square distribution for modeling axial data and also they derive the first two trigonometric moments for the proposed distribution in closed forms.