In this paper, an analytical solution is developed of the stress and displacement components in a three-dimensional solid disc subjected to Brazilian and point load test boundary conditions. The methodology is initially based on introducing the load distribution in both tests using the double Fourier series technique. The displacement vector in cylindrical polar coordinates (r, θ, z) is then presented by means of harmonic potentials according to the Papkovich-Neuber scheme. Stresses are then recovered by searching for acceptable potentials that satisfy both the domain Laplacian equation and the prescribed Fourier boundary expression. Several solutions are developed in terms of design graphs, and the effect of influencing parameters on the calculated results, e.g. material elastic properties, loading configurations and specimen geometries, are discussed.