A numerical technique was used to compute the supersonic and hypersonic, viscous flow fields around thin planar delta wings. These solutions were obtained by solving the Navier-Stokes equations subject to a conical approximation. The integration technique used was the MacCormack finite-difference scheme. Solutions were obtained for the upper-only, lower-only, and total flow fields around delta wings with supersonic leading edges. These solutions span a Mach number range of 2.94 to 10.17, a local Reynolds number range of 334,500 to 5,000,000, and various angles of attack from -15 to +15 deg. A stability criteria was developed and used which accounted for both the viscous and inviscid flow regions. Good agreement was obtained between the numerical results and experimental flow field data. The shock-induced vortex within the viscous region and the hypersonic viscous bubble on top of the boundary layer were computed, for the first time. A unique examination was made of the vortical singularities in the conical cross-flow plane of the delta wing. This investigation demonstrated the feasibility of applying the conical approximation to the Navier-Stokes equations in order to solve flow fields around thin delta wings.