A theoretical study of the bifurcation of the equilibrium state of straight coiled rods from an aging linear viscoelastic material is presented. The problem is formulated as the problem of eigenvalues of a homogeneous integral equation. The exact solution applies to rods with various types of end reinforcements and to any given creep function. The critical force is determined as a function of time. In the case of the Arutyunyan aging creep function, the influence of the loading moment is considered, as well as the influence of the values of the parameters that are in the creep function.