Abstract: A corresponding three-dimensional steady state model concerned with dendrite growth is analyzed considering the influence of a uniform convection field. By using Fourier series, an eight-order ordinary differential equation is finally solved and an accurate analytic solution is obtained in a very neat form. The correlations among coefficients in the analytic solution are determined. The obtained solution shows that the crystal growth in the steady state presents cyclic oscillation attenuation along the dendrite growth direction under the influence of a uniform fluid field, and this feature is an intrinsic character.