This study deals with the topic of “Analytical and numerical study of some problems in nonlinear mechanics." The study aimed to analyze a problem in nonlinear mechanics, which is “wave function collapse." Which is represented by the laboratory experiment "Schrödinger's cat", the interpretations of Heisenberg and Copenhagen, and an application of the method of Lagrange's equations to explain the phenomenon of wave function collapse and the EPR paradox, and Einstein's interpretation in pure algebraic theory and his interpretation of wave collapse, in addition to the Schrödinger equation. The study concluded with a set of results, the most important of which are: that the problem Wave function collapse represents one of the measurement problems in quantum mechanics. It has been proven that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The processes of particle creation and annihilation described based on quantum field theory play a major role in measurement processes. Decoherence theory also refers to the creation and annihilation of particles and these processes are a nonlinear consequence of quantum mechanics, in which case the wave function collapse term becomes a consequence of other statements of quantum mechanics rather than a separate assumption of quantum mechanics.