Sleep posture has a crucial impact on the incidence and severity of obstructive sleep apnea (OSA). Therefore, the surveillance and recognition of sleep postures could facilitate the assessment of OSA. The existing contact-based systems might interfere with sleeping, while camera-based systems introduce privacy concerns. Radar-based systems might overcome these challenges, especially when individuals are covered with blankets. The aim of this research is to develop a nonobstructive multiple ultra-wideband radar sleep posture recognition system based on machine learning models. We evaluated three single-radar configurations (top, side, and head), three dual-radar configurations (top + side, top + head, and side + head), and one tri-radar configuration (top + side + head), in addition to machine learning models, including CNN-based networks (ResNet50, DenseNet121, and EfficientNetV2) and vision transformer-based networks (traditional vision transformer and Swin Transformer V2). Thirty participants (n = 30) were invited to perform four recumbent postures (supine, left side-lying, right side-lying, and prone). Data from eighteen participants were randomly chosen for model training, another six participants’ data (n = 6) for model validation, and the remaining six participants’ data (n = 6) for model testing. The Swin Transformer with side and head radar configuration achieved the highest prediction accuracy (0.808). Future research may consider the application of the synthetic aperture radar technique.