Some bones of the body are constituted by cartilaginous supports in which growth is produced both with the ossification process that extends from the center of the bone towards its borders in a process so called endocondral ossification. In this period of bone tissue morphogenesis the factors controlling the process are mainly biochemical, and the mechanical influence is much lower. This paper presents a simulation model using reaction-diffusion equations for the growth and ossification process in the prenatal bone. It is primarily controlled by an interactive inhibitor-activator loop associated with the parathyroid hormone (PTHrP) and the Indian Hedgehog (Ihh). These equations in combination with the simulation of the proliferative process and the cartilage cell growth (chondrogenesis) lead to a quite accurate simulation of the growth process of a long bone, even predicting the development of secondary ossification centers in the epiphysis.