Continuum-mechanical models of musculoskeletal systems offer great potential to study the underlying biomechanics and physiology, investigate pathological conditions and patient-specific treatments, and accelerate the development of medical devices such as surgical tools, implants, or rehabilitation equipment for physical therapy. In anatomically complex joints such as the human shoulder, muscles play a critical role in both stabilizing inherently unstable articulations and enabling complex movement patterns through their coordinated interplay. Consequently, the formulation and parameterization of skeletal muscle constitutive models, such as the generalized active strain model we recently proposed [1], are critical for obtaining reliable predictions. However, the experimental data used to calibrate these skeletal muscle models exhibit significant variability, rendering the material parameters governing both passive and active muscle behavior highly uncertain. In addition, some parameters cannot be measured directly, further complicating the model development. Rather than relying on deterministic predictions, we adopt a probabilistic approach to modeling skeletal muscle tissue in complex musculoskeletal systems. We infer the posterior distributions of model parameters from experimental data through Bayesian calibration and perform global variance-based sensitivity analysis to identify influential and non-influential parameters [2]. To efficiently propagate uncertainty through computationally expensive finite element models, Gaussian process surrogate models are employed [3]. Based on the resulting model parameter distributions, we perform forward uncertainty quantification on physiologically representative subcomponent models of our continuum-mechanical human shoulder model [1] to assess variability in the model predictions. All probabilistic analyses are conducted using our open-source Python framework QUEENS [4], while the continuum-mechanical simulations are performed with our open-source multiphysics solver 4C [5]. Overall, our work demonstrates how Bayesian calibration, sensitivity analysis, and uncertainty quantification can enhance the robustness, interpretability, and reliability of continuum-mechanical musculoskeletal simulations, thereby supporting their application in biomechanical research and informed clinical decision-making.