This work reports the study of techniques for solving the Bethe-Salpeter equation with a confinement kernel and reports the foundation of a program for constructing a relativistic model of the hadrons based upon the Bethe-Salpeter equation. The techniques described here represent a solution of the problem of constructing a relativistic model for the mesons. General methods are given for defining a confinement kernel in momentum space, of transforming the confinement kernel into an integrodifferential operator, and for solving the integral equations which result from applying these procedures to the Bethe-Salpeter equation;Momentum space eigenfunctions for charmonium are obtained and found to be large out to momentum values of order 1GeV/c. The expectation values of both a relativistic and non-relativistic velocity operator are found to be greater than 0.48c for all of the states of charmonium investigated. The Lorentz structure of the confinement kernel is determined by a fit to the heavy meson spectra where it is found that inclusion of coupling of positive and negative frequency states appears to rule out a linear confinement kernel which contains a significant vector or pseudoscalar portion.