In this paper, the boundary element method has been applied to solve highly non-linear differential equations describing hydrodynamics and liquid/solid mass transfer at the wall of a packed-bed reactor with single-phase liquid flow. It is based on the boundary integral element concepts where both the dependent variable and its gradient become the primary variables. Two radial porosity profiles were used to take into account the non-uniformity character of the bed. It was shown that the computed velocity profiles have the same shape as the porosity profiles. The mass transfer experimental measurements, obtained for four different Schmidt numbers, are in good agreement with the computed predictions when uniform velocity profiles are used.