Neuronal responses of sensory cortex are highly variable, and this variability is correlated across neurons. To assess how variability reflects factors shared across a neuronal population, we analyzed the activity of many simultaneously recorded neurons in visual cortex. We developed a simple model that comprises two sources of shared variability: a multiplicative gain, which uniformly scales each neuron's sensory drive, and an additive offset, which affects different neurons to different degrees. This model captured the variability of spike counts and reproduced the dependence of pairwise correlations on neuronal tuning and stimulus orientation. The relative contributions of the additive and multiplicative fluctuations could vary over time and had marked impact on population coding. These observations indicate that shared variability of neuronal populations in sensory cortex can be largely explained by two factors that modulate the whole population.