Two-dimensional, supersonic flow field computation with by-pass holes has been conducted using Euler equation. An algorithm based on finite difference McCormack's technique is used to solve the subsonic-supersonic flow problem with and without by-passing. Trials on by-pass locations were also made. Operation without bypass shows the movement of the normal shock wave upstream which refers to an off-design operating regime. At a distance of 1.271 m measured from the cowl lip, the region of normal shock wave was localized near the throat which approximately represents the on-design perform 0ance condition (cells 8-9). When the flow is bypassed from the rear passages, the normal shock wave is sucked inside the flow passage save poor performance. Results show that by-passing provides a fast reaction to maintain a steady performance which meets the requirements of on-design operation. The Mach number variation corresponding to each case is presented. Results show that the tendency to unity Mach number near the cowl lip sector can be achieved using by-pass expelled. The influence of by-pass on the total pressure recovery and relative pressure is also discussed.