The segmentation of neck muscles is useful for the diagnoses and planning of medical interventions for neck pain-related conditions such as whiplash and cervical dystonia. Neck muscles are tightly grouped, have similar appearance to each other and display large anatomical variability between subjects. They also exhibit low contrast with background organs in magnetic resonance (MR) images. These characteristics make the segmentation of neck muscles a challenging task. Due to the significant success of the U-Net architecture for deep learning-based segmentation, numerous versions of this approach have emerged for the task of medical image segmentation. This paper presents an evaluation of 10 U-Net CNN approaches, 6 direct (U-Net, CRF-Unet, A-Unet, MFP-Unet, R2Unet and U-Net++) and 4 modified (R2A-Unet, R2A-Unet++, PMS-Unet and MS-Unet). The modifications are inspired by recent multi-scale and multi-stream techniques for deep learning algorithms. T1 weighted axial MR images of the neck, at the distal end of the C3 vertebrae, from 45 subjects with real-time data augmentation were used in our evaluation of neck muscle segmentation approaches. The analysis of our numerical results indicates that the R2Unet architecture achieves the best accuracy.