Abstract: This paper describes a time dependent numerical model for the steady and non-steady growthof a cellular/dendritic array in a moving linear temperature field. The model gives fully selfconsistent solutions for axisymmetric interface shapes, predicts cellular and dendritic spacings,undercoolings and the transition between structures. An important feature of the model is thatthe spacing selection mechanism has been treated. The model predicts two different dendriticgrowth regions. One occurs at low dimensionless velocities where the dendrite array is uniform:a small stable range of spacings is predicted and the prediction agrees very well with existing experiments. The other occurs at high dimensionless velocities where the dendrite array is irregular, its minimum spacing is inversely proportional to velocity Experiment was carried out to verify the prediction. The irregular dendrite array was observed and the measured minimum spacing fitted extremely well with the prediction. By fitting the numerical results. Relatively simple analytic expressions are obtained which provide an insight into the cellular and dendritic growth processes and are useful for comparing theory with experiment.