One of the most acute problems in studying composite stress-strain states is determining the initial residual stresses during the design of layered construction elements. The full stress–strain state of composite constructions consists of the initial (generated during the manufacturing process) and operating (generated during the working period) stages. A thorough investigation of the initial stage of the stress-strain state is very important to finding the total stresses and deformations, and determining the correct destruction time of composite structures, and preventing their destruction. Otherwise, if the initial stresses and deformations are not taken into account, the structures may be destroyed long before their expected service life.