This article examines the performance of shallow reinforced concrete shells with hinged supports along their perimeter. The relevance of this topic stems from the widespread use of such structures in modern construction for covering large buildings, as well as the insufficient understanding of their behavior under non-ideal boundary conditions. The aim of the study is to evaluate the stress-strain state and stability of the shells, taking into account geometric and physical nonlinearity, as well as the effect of long-term loads (concrete creep). The modeling was performed using the finite element method in the Pascal programming language based on DELPHI-7. The calculations take into account the rheological properties of concrete, nonlinear stress-strain relationships, and various loading schemes. Linear and nonlinear stability analyses were performed, including those involving the possible failure of supporting elements. The results showed that, when supported by a hinge, the shell loses stability under loads significantly lower than the design value, especially under long-term loads. The formation of characteristic localized dents and a loss of overall spatial performance of the structure were also detected. These data highlight the need for more accurate consideration of boundary conditions and nonlinear effects in the design of shallow shells. Recommendations are proposed for optimizing the shell shape and reinforcing the contour to improve its stability. The obtained results can be used in engineering practice for the analysis, design, inspection and safety of similar structures.