Context. During the formation of a star, material is ejected along powerful jets that impact the ambient material. This outflow phenomenon plays an important role in the regulation of star formation. Understanding the associated shocks and their energetic effects is therefore essential to the study of star formation. Aims. We present comparisons of shock models with observations of H 2 and SiO emission in the bipolar outflow BHR71. Such comparisons constitute a good way to constrain the type, velocity and age of the shock waves operating in this environment, as well as the physical conditions in the pre-shock region, e.g. density and magnetic field. They also provide a method for studying silicon in shocked regions. We make use of all the preliminary physical constraints obtained through such comparisons to predict water emission, under the basic assumption that the emission regions of the considered species coincide, at the resolution of currently available observations. Methods. New SiO observations from APEX are presented, and combined with Spitzer and ground-based observations of H 2 to constrain shock models. The shock regions associated with targeted positions in the molecular outflow are studied by means of a code that generates one-dimensional models of the propagation of stationary shock waves, and approximations to non-stationary ones. The emission of H 2 is dealt with in the code, whereas the emission of SiO and H 2 O are calculated by means of an external module, based on the LVG approximation. This external code provides local and integrated intensities for the lines of these species. A grid of models is used, covering shock velocities in the range 10 ≤ s ≤ 35 km s −1 , and pre-shock gas densities 10 4 ≤ n H ≤ 10 6 cm −3 . The magnetic field strength varies from about 45 μG to 600 μG. Results. The SiO emission in the inner part of the outflow is concentrated near the apex of the corresponding bow-shock that is also seen in the pure rotational transitions of H 2 . Simultaneous modelling is possible for H 2 and SiO and leads to constraints on the silicon pre-shock distribution on the grain mantles and/or cores. The best-fitting models are found to be of the non-stationary type, but the degeneracy of the solutions is still large. Pre-shock densities of 10 4 and 10 5 cm −3 are investigated, and the associated best-model candidates have rather low velocity (respectively, 20−30 and 10−15 km s −1 ) and are not older than 1000 years. We provide emission predictions for water, focusing on the brightest transitions, to be observed with the PACS and HIFI instruments of the Herschel Telescope.