The film thickness (t) dependence of the magnetic properties of La0.6Sr0.4MnO3 (LSMO) films grown on (001) MgO and (001) SrTiO3 substrates has been studied. Hysteresis loops measured at low temperature show a smooth increase of the retentivity accompanied by a decrease of the coercitive field as the film thickness increases. The increase of coercitivity with decreasing t can be interpreted in terms of a change in the domain structure of the films mainly due to an augmentation of domain pinning defects. The magnetic anisotropy has been measured using ferromagnetic resonance (FMR). A volume (VA) and a surface (SA) anisotropy contribution have been deduced from FMR angular dependence studies for both series of samples. In the LSMO films grown on MgO a VA component that corresponds to an easy-axis perpendicular to the plane of the films has been found while in contrast, the LSMO films grown on SrTiO3 present an easy-plane anisotropy. The SA is positive for both series favoring a perpendicular magnetic anisotropy. The measured magnetic anisotropy has been assigned to substrate-induced effects.