We present the first stage of an investigation of the interactions of the jets in the radio galaxy Hydra A with the intracluster medium. We consider the jet kinetic power, the galaxy and cluster atmosphere and the inner structure of the radio source. Analysing radio observations of the inner lobes of Hydra A by Taylor et al. we confirm the jet power estimates ∼1045 erg s−1 derived by Wise et al. from dynamical analysis of the X-ray cavities. With this result and a model for the galaxy halo, we explore the jet–intracluster medium interactions occurring on a scale of 10 kpc using two-dimensional, axisymmetric, relativistic pure hydrodynamic simulations. A key feature is that we identify the three bright knots in the northern jet as biconical reconfinement shocks, which result when an overpressured jet starts to come into equilibrium with the galactic atmosphere. Through an extensive parameter space study we deduce that the jet velocity is approximately 0.8c at a distance 0.5 kpc from the black hole. The combined constraints of jet power, the observed jet radius profile along the jet and the estimated jet pressure and jet velocity imply a value of the jet density parameter χ ≈ 13 for the northern jet. We show that for a jet β = 0.8 and θ = 42°, an intrinsic asymmetry in the emissivity of the northern and southern jet is required for a consistent brightness ratio ≈7 estimated from the 6-cm Very Large Array image of Hydra A.