The temporal response of an integrating cavity is examined and compared with the results of a Monte Carlo analysis. An important parameter in the temporal response is the average distance \overline{d} between successive reflections at the cavity wall; \overline{d} was calculated for several specific cavity designs—spherical shell, cube, right circular cylinder, irregular tetrahedron, and prism; however, only the calculation for the spherical shell and the right circular cylinder will be presented. A completely general formulation of \overline{d} for arbitrary cavity shapes is then derived, \overline{d}=4V/S where V is the volume of the cavity, and S is the surface area of the cavity. Finally, we consider an arbitrary cavity shape for which each flat face is tangent to a single inscribed sphere of diameter D (a curved surface is considered to be an infinite number of flat surfaces). We will prove that for such a cavity \overline{d}=2D/3 , exactly the same as \overline{d} for the inscribed sphere.