Viscous transonic flow-field simulations over wing-fuselage combinations were carried out using three-dimentional 'Reynolds averaged' Navier-Stokes equations. The LU-ADI factorization scheme which bas been developed and improved by the present authors was used for this study with an implimentation of new nonlinear smoothing terms. The computations were done for a practical wing-fuselage combination called "W-18", which was designed for the transonic transportation aircraft. The computed results reveal the effect of the existence of the fuselage near the junction of wing and fuselage. Each computation currently requires several hours of computer time, which is, however, quite reasonable when considering the number of grid points to be used for this study. The results indicate that the application of the present Navier-Stokes solution code to the complete aircraft geometries is quite promising.