Abstract: One key parameter for a radio astronomical telescope is its sensitivity, defined as the weakest detectable flux density of radiation. The CSRH is an interferometric array dedicated to solar observation in the centimeter to decimeter wavelength range. Different from other astronomical sources, the sun is a rather extended radio source, so the sensitivity analysis is necessary for system design and calibration of the CSRH. This paper describs the definition of the sensitivity and its physical meanings in cases of point sources and extended sources. More specifically, we analyze the sensitivity of interferometer and the image sensitivity for the CSRH. The weakest detectable flux density of the CSRH is about 0.08SFU to 0.23SFU within the 400MHz to 2GHz range. The signal-to-noise ratio in the input to the low-noise amplifier, which has an integrated bandwidth of 25MHz and an integration time of 3ms, is about 24dB. We finally give some examples to illustrate the effects of various system parameters (such as the amplitude slope, sinusoidal ripple, central-frequency displacement, phase variation, and delay-setting error) on the sensitivity of a radio interferometer.