Isotope shifts of the stable strontium isotopes Sr, Sr, Sr, and ' Sr and the radioactive isotopes Sr and Sr have been measured using laser spectroscopy on collimated atomic beams. The changes in mean square charge radii extracted from the isotope shifts show a pronounced shell effect at the closed neutron shell 1V =50. The experimental data are compared with the predictions of the droplet model and Hartree-Fock plus BCS calculations. The analysis suggests that the changes in mean square charge radii are due to a change in size, a change in the predominantly dynamic deformation, and a change in the diffuseness of the nuclear charge distribution.