Shear-wave elastography (SWE) is an imaging method that can be used to estimate shear wave speed and the Young’s modulus based on the measured shear wave speed under certain conditions. Up to date, no research has analyzed whether body composition factors contribute to ultrasound attenuation, refraction, reflection, and, consequently, SWE measurement errors. Therefore, this study aimed to analyze the association between demographic and body composition features with SWE errors for assessing the anterior scalene stiffness (which is a key structure in patients with neck pain and nerve compressive syndromes). Demographic (sex, age, height, weight, and body mass index), body composition (water volume, fat mass, and lean mass), and anterior scalene muscle stiffness (Young’s modulus and shear wave speed) data were collected from a sample of asymptomatic subjects. After calculating the absolute SWE differences between trials and the reliability estimates, a correlation matrix was generated to quantify the association among all the variables. A total of 34 asymptomatic subjects (24 males) were included in the analyses. Test–retest reliability was excellent for assessing the Young’s modulus and shear wave velocity (ICC = 0.912 and 0.923, respectively). No significant associations were found between age, height, weight, body mass index, body fat, lean mass, or water volume with SWE errors (p > 0.05). However, the Young’s modulus error was associated with the stiffness properties (p < 0.01), whereas shear wave speed was associated with none of them (all, p > 0.05). A detailed procedure can reliably assess the AS muscle stiffness. None of the sociodemographic or body composition features assessed were correlated with SWE errors. However, baseline stiffness seems to be associated with Young’s modulus error.