The general objective of the investigation reported in this thesis is to obtain a reliable understanding of the three dimensional potential flow through axial flow turbomachinery. The calculation of the three dimensional potential flow through an impeller is based on the method of distributed singularities. The blades are replaced by a series of line vortices and line sources which have their axes along the radial direction and are arranged along the blade camber surface. The basic perturbed velocity fields due to a single radial vortex line of constant strength and a single radial source line of variable strength along the radial direction are computed from a modified theory based on Tyson's and Rossow's formulation. Since the resultant perturbed flow fields are solutions of the linear Laplace equation and the boundary conditions are homogeneous, these solutions may be superimposed for a series of radial vortex lines and source lines located at arbitrary points. Eigen values and related functions are calculated for Bessel function of order m = 0 to 100, number of eigen values for each order of Bessel function n - 20, hub-to-tip ratio nu = 0.3, 0.6. A computer program to obtain the three dimensional flow field in a turbomachinery with arbitrary number of blades, number of singular points per blade, and singular points locations was developed. Examples illustrating the interference effects due to hub-to-tip ratio, stagger angle, numbers of the blades were carried out. The effects of the radial variation of the strength of the radial source line were examined. The three dimensional effects are found to be appreciable for low hub tip configuration with fewer number of blades. (Author).