Attenuation of gamma-rays by pair-production interactions in the intense magnetic field near pulsars leads to a sharp cut-off in the spectra predicted by polar cap models. Because the outer gap models do not predict such sharp cut-offs, the detection of pulsed VHE gamma-rays may be decisive in favoring the outer gap model over the polar cap model. Six pulsars are detected at EGRET energies and their high energy emission is already seriously constrained by the VHE upper limits. The excellent sensitivity and energy resolution of VERITAS should allow spectral measurements to be conducted even on these objects which are expected to have rapidly falling spectra in the VHE range. As such, VERITAS will provide detailed tests of the specific emission models.