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We investigate the constraints that can be placed on the distribution of dark matter around M87 using the 43 globular cluster velocities reported by Mould et al (1990). If the globular cluster system is assumed to be spherical, with an isotropic velocity distribution, we find that the most likely dependence of the dark matter density on radius is $r^{-1.8}$ between about 3 and 30 kpc, where the exponent lies between 0.2 and 3 with 99% confidence. We estimate that a sample of roughly 200 velocities would be necessary to determine the exponent of the density falloff to $\pm$ 0.5 under the isotropic hypothesis. The minimum number of velocities required to detect the presence of velocity anisotropy in the M87 globular cluster system is of order one thousand.
