This paper presents how incomplete wall contact between the foundation sidewalls and the surrounding soil alters the foundation input motion (FIM) of rectangular rigid boxes. The foundations are considered to have square sections embedded in a homogeneous linear half-space. The free-field motion (FFM) is assumed to be a vertical propagating shear wave. The foundation inputs in three translational and three rotational degrees of freedom (DOFs) were calculated using finite element analysis. Three additional net translational inputs were also introduced to cover movements along all six DOFs and remove the complexity of dealing with the rotational motions. Numerous models with incomplete soilfoundation contacts were constructed and related FIMs were examined numerically. The key results show that an incomplete contact can activate all six DOFs, even under translational FFM. In some cases, the net input motion reaches ordinates of four times the peak value counterpart in the FFM. This ratio, in perpendicular horizontal and, also, vertical directions, reaches 0.7 and 0.2, respectively. Given the field evidence observations, it is concluded that the odd trends reported in the literature for kinematic transfer functions (TFs), which have not been justified to date, may be caused by a partial soil-foundation contact.