We investigate numerically the effects of optical feedback on the intensity noise of vertical-cavity surfaceemitting lasers (VCSEL's) under single-mode and two-mode operations. Our model includes transverse effects such as carrier diffusion and spatial hole-burning. Results indicate that the relative-intensity noise is relatively unaffected at low feedback levels except for a narrowing and enhancement of the relaxationoscillation peak. At higher feedback levels, the VCSEL ceases to operate continuously, and its output becomes chaotic, following a period-doubling or a quasi-periodic route depending on the feedback level and the length of the external cavity. In the chaotic regime, the relative-intensity noise is enhanced by more than 20 dB. The critical feedback level at which the VCSEL output becomes chaotic depends on whether the laser operates in one or two transverse modes and how strongly these transverse modes are coupled through spatial holeburning.