Solving the inverse problem, finding the applied forces knowing the system characteristics and the response, has been a difficult problem in structural dynamics. Insufficient accuracy in the system identification and uncorrelated content in the response exacerbate the ill-conditioned nature of the indirect-force-determination problem. Numerical techniques for performing the force determination are exploited and compared. The characteristics of the force determination problems are investigated through least squares solution procedures and numerical examples. The credibility of the estimated forces are studied in the numerical examples using the correlations of the matrix condition number and the mode contribution factor with the resulting error. The focus of this research is the improved estimation of the applied forces. The two important factors in reducing the force determination error are accurate system identification and improved conditioning of the system matrix. A variety of techniques are examined to reduce the system identification error and control the response measurement uncertainty. The use of rotational or curvature degrees of freedom as an alternative to the translational degrees of freedom for the response measurements and for the structural dynamics model yields a quite differently conditioned system matrix. The choice of a particular degrees of freedom is shown to depend on the frequency contents of the applied forces. / Ph. D.