The results of a design study of a Hybrid Laminar Flow Control (HLFC) wing at transonic speed and correlative studies for finite, swept supersonic wings are discussed in this paper. Transonic HLFC wing was designed such as to obtain laminar laminar flow on the the wing upper surface for X/C of 0.6 and with suction applied from the leading edge to 60% of the chord and with suction applied from just aft of the leading edge to twenty-five percent of the chord. New theoretical methods have been recently developed for predicting pressure distributions, supersonic wave drag and transition location for finite swept wings at transonic and supersonic Mach number conditions and are illustrative computations are given. Results for laminar and turbulent boundary-layer parameters consisting of the displacement effects and skin friction drag are also presented. Theoretical methods developed for supersonic wings treat both sharp and blunt leading edges, under the assumption that the flow behind the curved shocks is rotational and non-isentropic. Computational results for transition, pressure distributions, and supersonic wave drag have shown excellent agreement with experimental data for supersonic wings with M varying from 1.9 M 4.04 and leading edge sweeps varying from 0° to 50°. Calculations have also been performed for the purpose of comparing the predicted aerodynamic performance of laminar-flow supersonic wings under the external disturbance environment existing in supersonic tunnels with free air conditions where external disturbances are negligible. Computed results indicate the necessity of a new design philosophy for maximizing L/D for laminar flow supersonic wings. Transonic theoretical capabilities are demonstrated through the design of an HLFC wing.