The prolate and oblate spheroidal functions are of importance in the analysis of electromagnetic or acoustical wave scattering from a spheroidal body and some boundary value problems involving a spheroidal body. In this paper

the program flowchart and some useful expressions for computing these two functions are presented

and the algorithms are discussed. The tabulations given earlier by C. Flammer have been extended

and the numerical values of the oblate as well as prolate radial and angular functions have been given to 8-digit accuracy.