Clinical and biological evidence suggest that the success of GRID therapy in debulking large tumors depends on the high peak-to-valley contrast in the dose distribution. In this study, we show that the peaks and valleys can be significantly blurred out by respiration-induced tumor motion, possibly affecting the clinical outcome. Using a kernel-based Monte Carlo dose engine that incorporates phantom motion, we calculate the dose distributions for a GRID with hexagonally arranged holes. The holes have a diameter of 1.3 cm and a minimum center-to-center separation of 2.1 cm (projected at the isocenter). The phantom moves either in the u parallel direction, which is parallel to a line joining any two nearest neighbors, or in the perpendicular u perpendicular direction. The displacement-time waveform is modeled with a cosn function, with n assigned 1 for symmetric motion, or 6 to simulate a large inhale-exhale asymmetry. Dose calculations are performed on a water phantom for a 6 MV x-ray beam. Near dmax, the static valley dose is 0.12D0, where D0 is the peak static dose. For motion in the u parallel direction, the peak and valley doses vary periodically with the amplitude of motion a and the transverse dose profiles are maximally flat near a=0.8 cm and a=1.9 cm. For the cos waveform, the minimum peak dose (Dpmin) is 0.67D0 and the maximum valley dose (Dvmax) is 0.60D0. Less dose blurring is seen with the cos6 waveform, with Dpmin=0.77D0 and Dvmax=0.45D0. For motion in the u perpendicular direction, the maximum flattening of dose profiles occurs at a=1.5 cm. GRIDs with smaller hole separations produce similar blurring at proportionally smaller amplitudes. The reported clinical response data from GRID therapy seem to indicate that mobile tumors, such as those in the thorax and abdomen, respond worse to GRID treatments than stationary tumors, such as those in the head and neck. To establish a stronger correlation between clinical response and tumor motion, and possibly improve the clinical response rates, it is recommended that prospective GRID therapy trials be conducted with motion compensation strategies, such as respiratory gating.