The technique of cavity quantum electrodynamics was proposed for coupling solid-state qubits. We study the prospects of employing superconducting stripline resonators as cavities for this purpose. The strong nonlinearity in these resonators originated by the effect of kinetic inductance may provide new tools for manipulating the state of the system and for measuring the outcome. Based on theoretical analysis and experimental results we show that such nonlinearity can be exploited for achieving strong intermodulation gain as well as quantum squeezing. Moreover, we demonstrate the ability to tune the mode frequencies of the resonator, which is needed for implementing these effects for coupling qubits.