In underground mining, rock mass stress is commonly modeled as a continuum. However, in block cave mining discrete modelling should be used to properly represent the stress over the extraction level in the broken column where there are high rock columns of large rock fragments. Unfortunately, we lack methods that use discrete modelling of stress in the broken column at block caving scale. In this work, we propose a vertical stress model of granular material to simulate static and dynamic flow conditions. The model is developed within a gravity flow simulator based on cellular automata to simulate the scale of the problem and flow conditions. The vertical stress model proposed is calibrated through four experimental models for the static condition. Then, based on the results from experimental testing, the dynamic condition is calibrated and compared with different flow scenarios. The results show that the proposed model can correctly simulate the vertical stresses in static conditions as well as dynamic conditions under the different flow setups tested. This vertical stress model with its flow simulator based on cellular automata has the potential to be applied at block caving scale once calibration parameters are defined.