The blood oxygen level‐dependent (BOLD) functional magnetic resonance imaging (fMRI) signal arises as a consequence of changes in cerebral blood flow (CBF) and cerebral metabolic rate of oxygen that in turn are modulated by changes in neural activity. Recent advances in imaging have achieved sub‐millimetre resolution and allowed investigation of the BOLD response as a function of cortical depth. Here, we adapt our previous theory relating the BOLD signal to neural activity to produce a quantitative model that incorporates venous blood draining between cortical layers. The adjustable inputs to the model are the neural activity and a parameter governing this blood draining. A three‐layer version for transient neural inputs and a multi‐layer version for constant or tonic neural inputs are able to account for a variety of experimental results, including negative BOLD signals.