This paper presents a method of computing the evolution of low mass stars from the main sequence to the helium flash. Many such computations are handicapped by the fact that the hydrogen burning shell source becomes very thin at a relatively early stage of evolution, and this means that either a very short time step is needed on the red giant branch, or else that some special method must be introduced. The present method has neither handicap: the same procedure is used whether there is a thin shell or not, and the time step can be chosen so that the overall structure of the star changes by a fixed small amount per step. About 100 or 150 steps are necessary to evolve a star to the helium flash. The basic features of the method are that the structure equations are solved using a non-Lagrangian mesh, so that a thin shell if it exists can move slowly through the mesh, even if it moves rapidly with respect to the mass coordinate; and that the composition and the mesh are solved simultaneously with the structure equations, giving greater stability and self-consistency. Although the work described here does not take account of convective mixing of composition, it is suggested that a simple generalization of the equations used here would give a reasonable treatment of both convective and semi-convective mixing, if they occur.