The steady three-dimensional stagnation-point flow and heat transfer of a dusty fluid toward a stretching sheet is investigated by using similarity solution approach. The freestream along z-direction impinges on the stretching sheet to produce a flow with different velocity components. The governing equations are transformed into ordinary differential equations by introducing appropriate similarity variables and an exact solution is obtained. The nonlinear ordinary differential equations are solved numerically using Runge–Kutta fourth-order method. The effects of the physical parameters like velocity ratio, fluid and thermal particle interaction parameter, ratio of freestream velocity parameter to stretching sheet velocity parameter, Prandtl number, and Eckert number on the flow field and heat transfer characteristics are obtained, illustrated graphically, and discussed. Also, a comparison of the obtained numerical results is made with two-dimensional cases existing in the literature and good agreement is approved. Moreover, it is found that the heat transfer coefficient and shear stress on the surface for axisymmetric case are larger than nonaxisymmetric case. Also, for stationary flat plat case, a similarity solution is presented and a comparison of the obtained results is made with previously published results and full agreement is reported.