Preterm birth is the leading cause of childhood mortality and can lead to health risks in survivors. The mechanical functions of the uterus, fetal membranes, and cervix have dynamic roles to protect the fetus during gestation. To understand their mechanical function and relation to preterm birth, we built a three-dimensional parameterized finite element model of pregnancy. This model is generated by an automated procedure that is informed by maternal ultrasound measurements. A baseline model at 25 weeks of gestation was characterized, and to visualize the impact of cervical structural parameters on tissue stretch, we evaluated the model sensitivity to (1) anterior uterocervical angle, (2) cervical length, (3) posterior cervical offset, and (4) cervical stiffness. We found that cervical tissue stretching is minimal when the cervical canal is aligned with the longitudinal uterine axis, and a softer cervix is more sensitive to changes in the geometric variables tested.