The medical training concerning childbirth for young obstetricians involves performing real deliveries, under supervision. This medical procedure becomes more complicated when instrumented deliveries requiring the use of forceps or suction cups become necessary. For this reason, the use of a versatile, configurable childbirth simulator, taking into account different anatomical and pathological cases, would provide an important benefit in the training of obstetricians, and improve medical procedures. The production of this type of simulator should be generally based on a computerized birth simulation, enabling the computation of the reproductive organs deformation of the parturient woman and fetal interactions as well as the calculation of efforts produced during the second stage of labor. In this paper, we present a geometrical and biomechanical modeling of the main parturient's organs involved in the birth process, interacting with the fetus. Instead of searching for absolute precision, we search to find a good compromise between accuracy and model complexity. At this stage, to verify the correctness of our hypothesis, we use finite element analysis because of its reliability, precision and stability. Moreover, our study improves the previous work carried out on childbirth simulators because: (a) our childbirth model takes into account all the major organs involved in birth process, thus potentially enabling different childbirth scenarios; (b) fetal head is not treated as a rigid body and its motion is computed by taking into account realistic boundary conditions, i.e. we do not impose a pre-computed fetal trajectory; (c) we take into account the cyclic uterine contractions as well as voluntary efforts produced by the muscles of the abdomen; (d) a slight pressure is added inside the abdomen, representing the residual muscle tone. The next stage of our work will concern the optimization of our numerical resolution approach to obtain interactive time simulation, enabling it to be coupled to our haptic device.