An apparatus for treating fixed biological tissue to inhibit calcification of the biological tissue following implantation thereof in a mammalian body. The apparatus includes a container for placing the biological tissue in contact with a treatment solution, structure to induce relative tissue/solution movement, and structure to heat the solution. The relative movement may be induced by shaking a container in which the tissue is immersed in the treatment solution, or by stirring the solution within the container. The movement may also be induced by flowing a treatment solution past the tissue to be treated. The tissue may be free to move in the treatment container, or may be restrained from gross movements. The flow may be part of a circulation system having a reservoir, with a heater being provided to heat the treatment solution in the reservoir. Alternatively, a treatment apparatus, including a fluid circulation system if desired, may be enclosed in an incubator. The tissue may be mounted in a planar configuration generally parallel to the direction of fluid flow. A flow column having a plurality of sections divided by perforated baffles may be used to treat multiple tissues at once.