Biomedical materials are encapsulated in ionically crosslinked polymer capsules, preferably alginate microcapsules. The alginate capsules are then subjected, in a liquid vehicle, to an ethylenically unsaturated monomer and an initiator, to induce polymerization of the unsaturated monomer and therey enhance the strength of the capsule wall. The microcapsules can be after-treated with, for example, polysine and alginate to reduce their tendency to elicit an immune response if implanted in an animal. The invention extends to the microcapsules and also to a method of treating or preventing medical conditions in an animal particularly a human, by implanting microcapsule containing biomedical material in the animal.