We calculated the form of absorption bands of RbCs molecules attached to the surface of cold helium droplets. The influence of the helium cluster was taken into account by treating the cluster as a finite-size cryostat and by anticipating the broadening effects which yield continuum bands. Thus, only the lowest vibrational wave functions of the lowest singlet and triplet electronic states were taken into account. The calculations are limited to the Hund's coupling case a, with neglected spin-orbit interaction and assuming constant transition-dipole-moment functions, which can serve as the first approximation to be compared with future experimental results. (c) 2007 Elsevier B.V. All rights reserved.