We discuss the short-time response of a multicellular spheroid to an external pressure jump. Our experiments show that 5 min after the pressure jump, the cell density increases in the centre of the spheroid but does not change appreciably close to the surface of the spheroid. This result can be explained if the cells are polarized which we show to be the case. Motivated by the experimental results, we develop a theory for polarized spheroids where the cell polarity is radial (except in a thin shell close to the spheroid surface). The theory takes into account the dependence of cell division and apoptosis rates on the local stress, the cell polarity and active stress generated by the cells and the dependence of active stress on the local pressure. We find a short-time increase of the cell density after a pressure jump that decays as a power law from the spheroid centre, which is in reasonable agreement with the experimental results. By comparing our theory to experiments, we can estimate the isotropic compression modulus of the tissue.