We present a new approach to study the properties of the sun. We consider small variations of the physical and chemical properties of the sun with respect to Standard Solar Model predictions and we linearize the structure equations to relate them to the properties of the solar plasma. By assuming that the (variation of) the present solar composition can be estimated from the (variation of) the nuclear reaction rates and elemental diffusion efficiency in the present sun, we obtain a linear system of ordinary differential equations which can be used to calculate the response of the sun to an arbitrary modification of the input parameters (opacity, cross sections, etc.). This new approach is intended to be a complement to the traditional methods for solar model calculation and allows to investigate in a more efficient and transparent way the role of parameters and assumptions in solar model construction. We verify that these Linear Solar Models recover the predictions of the traditional solar models with an high level of accuracy.