The paper presents a general algorithm for constructing fundamental solutions to the equations of the theory of thin isotropic shells. Fundamental solutions are solutions to problems about the impact of an instantaneous concentrated load on a shell. The fundamental solutions are obtained using the method of integral transformations together with the method of O. Marichev for calculating improper integrals of special functions. It was proposed to expand the methodology for constructing fundamental solutions to the dynamics of shells in the case of the action of a static force load on a thin flat shell made of an isotropic material. The solution was obtained analytically in the form of series for a special function of hypergeometric type. It’s possible to clarify previously known results using the obtained solution, when the fundamental solution to the statics of thin shells is expressed through a modified Bessel function of the second kind. A number of options for writing the fundamental solution allows to select a more efficient computational algorithm for the numerical solution of applied problems (for example, Boundary element method) since the fundamental solution is written in the form of a functional series, and not expressed as a separate function.