Abstract: Directional solidification is a relatively effective technical means of controlling the solidification speed and adjusting the temperature distribution to enable crystals to grow in the desired solidification direction. During directional solidification, a flow field is inevitably generated, and under the influence of the flow field, the growth of deep cellular crystals will deviate from the original growth trajectory. It is necessary to study the growth morphology of deep cellular crystals in directional solidification under the influence of flow field in order to obtain the crystals required for production. This article uses the matching asymptotic expansion and multivariate asymptotic expansion methods to obtain the asymptotic solution of the concentration field in the external region of deep cellular crystal under the influence of far field flow during directional solidification, the quantization conditions under the influence of flow field, the external solution of the interface shape function, and the internal solution of the root region. By matching the internal and external solutions, an approximate solution of the overall interface shape of deep cellular crystal growth was obtained; Under different flow intensities, the effect of far field flow on the morphology of deep cellular crystal growth was studied. The results showed that far field flow has a significant impact on the growth of deep cellular crystals in directional solidification. With the increase of flow intensity, the cellular crystal spacing gradually decreases and the curvature at the bottom of the root increases; The tip radius decreases with the increase of flow intensity, and the cellular crystal tends to elongate.