The main purpose of the study is to develop models for the strength reliability of closed spillways at earth-fill dams. The object of the research is closed mine-type spillway structures. The strength reliability model of a closed spillway structure includes a material model, a shape model, a model of actual load, and a fracture model. The material model in most cases is reinforced concrete. The shape model is very important, especially for precast culverts of glory hole spillways, because giving it a certain shape can significantly reduce the value of stresses acting in weak sections. As a result of the stress reduction, there is a decrease in material requirements, primarily for metals, leading to reduced energy and economic costs. This also makes it possible to increase the reliability and durability of such structures, increase their operational safety, and adapt them to various operating conditions. The shape model for the culvert is justified. The load model determines the behavior of the structure during construction and operation. This article suggests a justification for the methodology for calculating the strength of a precast culvert of segment blocks. The methodology allows to perform strength analysis of culverts of closed spillways with a cross-section outline similar to a membrane. The state of reinforced concrete load-carrying units under various combinations of loads has been studied. The limits of stresses and displacements, the excess of which can lead to destruction in the load-carrying units, are determined.