Despite recent major advances, the opacity remains an important source of uncertainty in the calculation of solar models, and hence of solar oscillation frequencies. Hence it is of substantial interest to investigate the sensitivity of solar structure to changes in the opacity. Furthermore, we may hope from the precise helioseismic inferences of solar structure to obtain information about possible corrections to the opacities used in the model calculation. Here we carry out detailed calculations of the influence on solar models of changes in the opacity, including also evolutionary effects. We find that over the relevant range the response of the model is approximately linear in the opacity change, allowing the introduction of opacity kernels relating a general opacity change to the corresponding model changes. Changes in the convection zone can be characterized entirely by the change in the initial composition and mixing length required to calibrate the model.