The problem of the origin of the upper cutoff in the spectrum of multi-GeV solar protons is examined. This analysis concerns the case in which the upper cutoff is determined at the source level by a stochastic mechanism of acceleration. The operation of the random process at the solar source is justified in terms of a small length scale of the fluctuations of the magnetic field. The deviation of the particle spectrum from a perfect power law is explained by a discontinuity in the behavior of the mean free path of particles for acceleration. The assumption that this random acceleration step depends highly on the medium density (1013 cm-3) and magnetic field strength (500 G) leads us to estimate a maximum rigidity greater than the measured value. We also found that the upper cutoff is imposed not by the linear dimension of the source but by this characteristic length scale of turbulence therein and that the source dimension is somewhat smaller than is usually thought. From the magnitude of some physical parameters of the source estimated in this paper the scale of turbulence of the magnetic field of about 1 km seems to be an interesting result within the framework of stochastic acceleration theory.