Microbially induced calcite precipitation is a soil reinforcement technique where bacteria are used to produce calcium carbonate, precipitated after the hydrolysis of urea promoted by the enzyme urease present in the microorganisms. This biocement clogs the soil pores and bonds its grains, causing an increase of the soil strength and stiffness and a decrease of its permeability. To analyse the precipitation process, a model of a two-phase porous medium, where each phase is composed of several species, is created. The solid phase is composed by soil particles, bacteria and calcite while the fluid phase contains water, urea and other dissolved species that are present in the biochemical reaction. A finite element formulation embodying water seepage, advective diffusion of species and soil deformation is proposed to compute the generation of solid mass (the biocement), and numerical simulations are presented to analyse the process under various conditions (e.g. different bacteria dosages, feeding frequency and composition). The results of the numerical simulations are also compared to results available in the literature obtained with models that only address diffusion couplings and where soil deformation is not accounted for.