Abstract We study resonant response of an oscillator with shot-noise type mass fluctuations. The model describes a nano-mechanical resonator with adsorbing and desorbing molecules. We derive an analytical expression for the spectrum of the oscillator. It applies to an arbitrary interrelation between the damping rate of the oscillator, the adsorption and desorption rates and the magnitude of frequency shift due to a single adsorption or desorption event. Depending on this interrelation the spectrum may display fine structure corresponding to variation of the number of adsorbed molecules or present a single asymmetric peak. The results can be used for high-precision fast measurements of molecular mass with nano-mechanical resonators.