Rheological models are used to represent different scanning probe microscope configurations. The solutions for their static and dynamic behavior are found and used to analyze which scanning probe microscope configuration is best for a given application. We find that modulating the sample at high frequencies results in the best microscope behavior for measuring the stiffness of rigid materials, and that by modulating the tip at low frequencies and detecting the motion of the tip itself (not its position relative to the tip holder) should be best for studying compliant materials in liquids.