Preterm birth is the most common cause of neonatal death. Current diagnostic methods that assess the risk of preterm birth involve the collection of maternal characteristics and transvaginal ultrasound imaging conducted in the first and second trimester of pregnancy. Analysis of the ultrasound data is based on visual inspection of images by gynaecologist, sometimes supported by hand-designed image features such as cervical length. Due to the complexity of this process and its subjective component, approximately 30% of spontaneous preterm deliveries are not correctly predicted. Moreover, 10% of the predicted preterm deliveries are false-positives. In this paper, we address the problem of predicting spontaneous preterm delivery using machine learning. To achieve this goal, we propose to first use a deep neural network architecture for segmenting prenatal ultrasound images and then automatically extract two biophysical ultrasound markers, cervical length (CL) and anterior cervical angle (ACA), from the resulting images. Our method allows to estimate ultrasound markers without human oversight. Furthermore, we show that CL and ACA markers, when combined, allow us to decrease false-negative ratio from 30% to 18%. Finally, contrary to the current approaches to diagnostics methods that rely only on gynaecologist's expertise, our method introduce objectively obtained results.