Objective. To work out as close as possible to normal human anatomy three-dimensional finite element model of the shoulder joint with elastic ligaments as well as with muscles and the spatial location of their attachment points, to analyze the stress-strain state of the element proximal humerus and scapula. Methods. A geometric model of the humerus and scapulae are constructed. The three-dimensional modeling of the shoulder join based on the geometric models  was used with software SolidWorks with mathematical modeling method finite elements and the stress-strain state analysis in the applicationpackage Ansys software. To approach the real conditions of the model we have added the elastic elements that mimic muscles. Model loaded with forces that reproduce the effort in the muscles, applied to the respective contact planes on the humerus head of the human bone. The stress-strain state of proximal elements is calculated in the humerus and scapula for the angles of the abduction  — 0 °, 30°, 60° and 90° in neutral rotation of the humerus.Results. The tensile stresses in the scapula are distributed in such a way that at an angle of 0 ° the limb is not raised +5.67 MPa in the area below the joint depressions. The minimum values of the compressive stress have been reached 18.5 MPa. Maximum stresses are in 1.5–2 times higher area of the articular cartilage of the humerus head compared to the cartilage of the glenoid cavity of the scapula. It is established that the dependence of the valuesof the area of the contact zone in the range of change limb abduction angle (0° ... 90°) can be approximated section of a cubic parabola, with changes in area insignificant and are equal to +2.26% — 7.3 % of the value in neutral position at an angle of 0°. Minor differences with the results of similar studies indicate that the validity of the developed mathematical model. Conclusions. The proposed model would allow performing more correct mathematical modeling and comparative analysis of the stress-strain state for various methods of surgical treatment of pathology shoulder joint, in particular arthroplasty.