The transverse bending of cylindrical tubes embedded in Winkler elastic foundation was studied based on the higher-order shear deformation beam theory. A governing equation for bending of circular cylindrical tubes on elastic foundation or in a surrounding Winkler matrix was derived and accurate solutions were presented for four typical boundary conditions. The obtained results show that the shear stress τ_xr automatically vanishes on the inner and outer surface of cylindrical tubes when an appropriate warping shape function instead of the shear correction coefficient is chosen. And it can provide analytical solutions with sufficient accuracy for the bending problems of cylindrical tubes with different length-diameter ratios and thickness-diameter ratios. When the stiffness coefficient approaches zero, the deflection curve of cylindrical tube embedded in Winkler elastic foundation approaches the deflection curve of cylindrical tube placed in free space, which verifies the accuracy of the present method. Different from the Euler-Bernoulli beam theory, the normal stress over the cross-section is no longer linear with the abscissa from the neutral surface in this method, and it is especially obvious when the length-diameter ratio is small and the thickness-diameter ratio is large.The shear stress τ_xz decreases when the distance from the neutral surface becomes large, approaching zero at the top and bottom positions, and the maximum shear stress occurs at the neutral surface which is close to the inner surface.