In a commercially available CSR controlled stress rheometer, the theoretical formulae for calculating the shear viscosity and complex viscosity of a fluid in a recessed concentric cylinder geometry, do not take into account end effects. The first part of this paper is concerned with a theoretical prediction of end effects on steady shear viscosity measurements of Newtonian fluids in a recessed concentric cylinder geometry. Fluid inertia effects are included in the theory and the relevant equations are solved using a perturbation analysis which is valid for low Reynolds number hows. The perturbation equations are solved numerically using a finite difference method. From this theory, correction formulae are produced to compensate for end effects and second order fluid inertia effects in steady shear flows on a CSR rheometer. End effects are also investigated for shear thinning fluids using the Polyflow package, and results show that they are less significant than those for Newtonian fluids. The second part of this paper is concerned with a theoretical prediction of the end effect of a recessed concentric cylinder geometry on complex viscosity measurements of a generalised linear viscoelastic fluid. The theory will include a first and second order fluid inertia perturbation analysis and the relevant equations are solved using a finite difference method. Using this theory, the existing oscillatory shear formulae which include second order fluid inertia effects, are modified to compensate for end effects.