Blood oxygenation level dependent (BOLD) functional MRI has been used for inferring layer specific activation in humans. However, intracortical veins perpendicular to the cortical surface are suspected to degrade the laminar specificity as they drain blood from the microvasculature and BOLD signal is carried over from lower to upper cortical layers on its way to the pial surface. In this work, a vascular model of the cortex is developed to investigate the laminar specificity of the BOLD signal for Spin Echo (SE) and Gradient Echo (GE) following the integrative model presented by Uludağ et al. (2009). The results of the simulation show that the laminar point spread function (PSF) of the BOLD signal presents similar features across all layers. The PSF for SE is highly localised whereas for GE there is a flat tail running to the pial surface, with amplitude less than a quarter of the response from the layer itself. Consequently the GE response at any layer will also contain a contribution accumulated from all lower layers.