The overall rate constant of reaction of diffusing species in regular arrays of spherical particles is investigated. The surface reaction occurring on the particle surface is of finite rate. Calculation results for three common spherical arrays: Simple cubic (SC), face-centered cubic (fcc), and body-centered cubic (bcc) arrays, are illustrated and studied. The normalized overall rate constant, k/k(0), is found to be a function of the particle volume fraction, a dimensionless parameter P characterizing the relative rate of diffusive transport versus surface reaction, and the array structure. When the process is diffusion limited(P = 0), results from the present development agree very well with those from first passage time simulations. When it is surface reaction limited (P-->infinity), the normalized overall rate constant is shown to exactly equal 1/(1-f), independent of the system structure. For general P, results of the present study conform well with Torquato and Avellaneda's upper bound [J. Chem. Phys. 95, 6477 (1991)]. The normalized overall rate constant increases with increasing f, but decreases with increasing P. For the three arrays, the magnitudes of k/k(0), at the same f and P, are in the order of bcc approximate to fcc>SC. As P increases, the structural effect on k/k(0) weakens.