We study effects of turbulent mixing on the random growth of an interface. The growth is describedby the Wolf model [Phys. Rev. Lett. 67: 1783 (1991)] – anisotropic generalisation of Kardar–Parisi–Zhang model. The turbulent advecting velocity field is modelled by the anisotropic Avellaneda-Majdaensemble [Commun. Math. Phys. 131: 381 (1990)]: Gaussian statistics with the correlation functionhvvi / (t t0)(kk)n; kd+1? , where nboldsymbolk is the wave vector, nboldsymbolk = nboldsymbolk? +nboldsymbolnkk, nboldsymboln is a preferred direction, and 0 < <2 is a free parameter. Using thefield theoretic renormalization group we establish existence of the fixed points both for the model withoutadvection and for the model with it – in the former case the results are in a good qualitative adreement withthose of Wolf. Addition of the velocity field destroys stability of the fixed points. The fixed point coordinatesand their regions of stability are calculated to the first order of the (double) expansion in ( a