[en] The measure of the third-order structure function, $\mathit{Y}$, is employed in the solar wind to compute the cascade rate of turbulence. In the absence of a mean field $B_0=0$, $\mathit{Y}$ is expected to be isotropic (radial) and independent of the direction of increments, so its measure yields directly the cascade rate. For turbulence with mean field, as in the solar wind, $\mathit{Y}$ is expected to become more two-dimensional (2D), that is, to have larger perpendicular components, losing the above simple symmetry. To get the cascade rate, one should compute the flux of $\mathit{Y}$, which is not feasible with single-spacecraft data; thus, measurements rely on assumptions about the unknown symmetry. We use direct numerical simulations (DNSs) of magnetohydrodynamic (MHD) turbulence to characterize the anisotropy of $\mathit{Y}$. We find that for strong guide field $B_0=5$ the degree of two-dimensionalization depends on the relative importance of shear-Alfvén and pseudo-Alfvén polarizations (the two components of an Alfvén mode in incompressible MHD). The anisotropy also shows up in the inertial range. The more $\mathit{Y}$ is 2D, the more the inertial range extent differs along parallel and perpendicular directions. We finally test the two methods employed in observations and find that the so-obtained cascade rate may depend on the angle between B₀ and the direction of increments. Both methods yield a vanishing cascade rate along the parallel direction, contrary to observations, suggesting a weaker anisotropy of solar wind turbulence compared to our DNSs. This could be due to a weaker mean field and/or to solar wind expansion.