Three-dimensional Euler and Full Navier-Stokes computational procedures have been utilized to simulate the flow field in an axial compressor cascade with tip clearance. An embedded H-grid topology was utilized to resolve the flow physics in the tip gap region. The numerical procedure employed is a finite difference Runge-Kutta scheme. Available measurements of blade static pressure distributions along the blade span, dynamic pressure and flow angle in the cascade outlet region, and spanwise distributions of blade normal force coefficient and circumferentially averaged flow angle are used for comparison. Several parameters which were varied in the experimental investigations were also varied in the computational studies. Specifically, measurements were taken and computations were performed on the configuration with and without: tip clearance, the presence of an endwall, inlet endwall total pressure profiles and simulated relative casing rotation. Additionally, both Euler and Navier-Stokes computations were performed to investigate the relative performance of these approaches in reconciling the physical phenomena considered. Results indicate that the Navier-Stokes procedure, which utilizes a low Reynolds number k-e model, captures a variety of important physical phenomena associated with tip clearance flows with good accuracy. These include tip vortex strength and trajectory, blade loading near the tip, the interaction of the tip clearance flow with passage secondary flow and the effects of relative endwall motion. The Euler computation provides good but somewhat diminished accuracy in resolution of some of these clearance phenomena. It is concluded that the level of modelling embodied in the present approach is sufficient to extract much of the tip region flow field information useful to designers of turbomachinery.