A stochastic “Fubini” lemma and an approximation theorem for
integrals on the plane are used to produce a simulation algorithm
for an anisotropic fractional Brownian sheet. The convergence rate
is given. These results are valuable for any value of the Hurst
parameters $(\alpha_1,\alpha_2)\in ]0,1[^2,\alpha_i\neq\frac{1}{2}.$
Finally, the
approximation process
is iterative on the quarter plane $\mathbb {R}_+^2.$
A sample of such simulations can be used to test estimators
of the parameters αi,i = 1,2.