Plant morphogenesis is the development of plant form and structure by coordinated cell division and growth. We present a dynamic computational model of plant morphogenesis at cellular level. The model is based on a self- reproducing cell, which has dynamic state parameters and spatial boundary geometry. Cell-cell signalling is simulated by diffusion of morphogens, and genetic regulation by a program or script. Each cell runs an identical script, equivalent to the genome. The model provides a platform to explore coupled interactions between genetic regulation, spatio-mechanical factors, and signal transduction in multicellular organisation. We demonstrate the capacity of the model to capture the key aspects of plant morphogenesis.