The linear disturbance development of cross-flow instability for compressible flows on infinite span swept wings with a biconvex airfoil is investigated using Linear Stability Theory (LST). The main goal of the investigations was to explore the effects of the wing sweep angle and the airfoil thickness to chord ratio, and to provide a general overview of the linear cross-flow instability for the infinite span swept wing with biconvex airfoil. The LST results obtained indicate the presence of a strong cross-flow instability for the airfoils and sweep angles considered. As expected, the cross-flow instability becomes stronger for an increasing sweep angle and larger thickness to chord ratios of the airfoil. For outboard travelling modes (positive spanwise wavenumbers), it was shown that unsteady cross-flow disturbances became unstable further upstream than steady disturbances. On the other hand, for inboard travelling modes (negative spanwise wavenumbers), steady cross-flow disturbances became unstable further upstream than unsteady disturbances. Overall, the unsteady cross-flowdisturbances with positive spanwise wavenumbers had the largest growth rates and N-factors.