We present the results of stellar evolution calculations which show quantitatively how the measured abundances of lithium and beryllium in low-mass stellar objects can be used to discriminate between brown dwarfs and low-mass main-sequence stars. The evolution of boron, although less useful in this regard, is also studied. We define a transition mass range, below which at least 50% of the light element remains at the end of nuclear burning, and above which no more than 10% remains. We find that the transition mass range for Li burning is 0.059-0.062 M., while for Be the range is 0.075-0.077 M.. Using these results, we then examine the factors (e.g., age and luminosity) that affect our ability to identify low-luminosity objects as brown dwarfs. In particular, we show that the lithium test would be well suited for brown dwarf candidates located in nearby open clusters with ages in the range of 2 x 10(8)-5 x 10(8) yr.