When two successive stimuli are presented within 0-200 ms intervals, the recognition of the first stimulus (the target) can be impaired by the second (the mask). This backward masking phenomenon has a form called metacontrast masking where the target and the mask are in close spatial proximity but not overlapping. In that case, the masking effect is strongest for interval of 60-100 ms. To understand this behaviour, activity propagation in a feedforward network of leaky integrate and fire neurons is investigated. It is found that, if neurons have a selectivity similar to that of V1 simple cells, activity decays layer after layer and ceases to propagate. To combat this, a local amplification mechanism is included in the model, using excitatory lateral connections, which turn out to support prolonged self-sustained activity. Masking is assumed to arise from local competition between representations recruited by the target and the mask. This tends to interrupt sustained firing, while prolonged retinal input tends to re-initiate it. Thus, masking causes a maximal reduction of the duration of the cortical response to the target towards the end of the retinal response. This duration exhibits the typical U-shape of the masking curve. In this model, masking does not alter the propagation of the onset of the response to the target, thus preserving response reaction times and enabling unconscious priming phenomena.