In this paper, the problem of a simple oscillator traversing an elastically supported continuum is investigated. Numerical results for the shear force distribution of the continuum are obtained. To circumvent convergence difficulties associated with the evaluation of the shear force, an improved series expansion is derived. Effects of boundary flexibility on the shear force spatial and temporal distributions, as well as the series convergence properties, are examined. Results reveal the presence of a high amplitude, high frequency component in the shear force due to significant contributions of the higher order modal terms in the series expansion. This is important from the viewpoint of understanding the cumulative fatigue failure of the continuum. A useful and compact formula estimating the value of the support stiffness above which the boundary can be idealized as simply supported is also derived.