Numerical solutions of the Navier-Stokes equations are obtained for an axisymmetric nozzle in a supersonic external flowfield (M^ =1.94, My =3.0, Re^ =2.2xl0). Five jet pressure ratio conditions ranging from a highly overexpanded case that exhibits a Mach disk shock formation to a slightly underexpanded case are solved computationally. MacCormack's explicit finite-difference algorithm, an adaptive grid scheme, and locally dependent eddy viscosity modeling are utilized to obtain the numerical solutions. The computational results accurately reproduce the experimentally observed viscous effects on the nozzle base pressure and shock locations resulting from a thick base annulus on the nozzle. Correct transition from regular shock reflection to Mach disk reflection in the jet core was achieved numerically.