We present two methods by which single cells can be mechanically trapped and continuously monitored within the suspended microchannel resonator (SMR) mass sensor. Since the fluid surrounding the trapped cell can be quickly and completely replaced on demand, our methods are well suited for measuring changes in cell size and growth in response to drugs or other chemical stimuli. We validate our methods by measuring the density of single polystyrene beads and Saccharomyces cerevisiae yeast cells with a precision of approximately 10(-3) g cm(-3), and by monitoring the growth of single mouse lymphoblast cells before and after drug treatment.