The dissertation is concerned with the determination of the transient strain and deflection in a beam after reflection from the boundaries occur but before the steady state condition prevails. An adequate existing theory was sought which will predict with reasonable accuracy these transient strains and displacements. Corresponding measured values were obtained and used to check the theory. It was concluded that: (1) Although the Mindlin-Goodman theory correctly predicts the general shape of the elastic curve, the displacement magnitudes cannot be accurately determined using 5-place floating point arithmetic. (2) It appears unlikely that usable strain values can be obtained by this method, even with the use of double precision arithmetic on a computer. (3) Practical considerations make it necessary to use a high speed, electronic, digital computer to obtain deflection values from the Mindlin-Goodman solution. (4) Even for a relatively simple structure and loading, the solution is more cumbersome and complicated than is consistent with ordinary engineering usage. (Author).