A Stokesian dynamics constraint algorithm for the irreversible deposition of colloidal particles onto a surface is presented. This algorithm can also be used to simulate a variety of nondeposition phenomena and with any method for computing the hydrodynamic interactions among the particles. In particular, a multipole scheme we recently described for computing the mobility matrix of colloidal particles, with or without the presence of a wall, is used here in conjunction with the new deposition algorithm to perform Stokesian dynamics irreversible deposition simulations on a group of 75 colloidal particles. Deposition simulations are performed with and without the hydrodynamic effect of the wall (substrate) being included in the mobility matrix. The results of the simulations lead to important qualitative conclusions on the effect of hydrodynamic interactions on the deposition process, in particular the hydrodynamic effect of the wall. In addition, the simulations serve to illustrate the performance of the new deposition algorithm.