A hybrid model, which combines a bead-and-spring approach with the breathing sphere model, is developed for a molecular dynamics study of matrix-assisted laser desorption of analyte molecules. The combined model is used to investigate the initial stage of analyte molecular ejection at different laser fluences. Analyte molecules embedded near the irradiated surface are lifted off at laser fluences corresponding to the ablation threshold. Higher fluences are required to eject analyte molecules embedded deeper below the surface. At all considered laser fluences, analyte molecules are ejected within matrix clusters, thus solvated. The degree of solvation decreases with increasing laser fluence and during the ablation plume expansion. Possible mechanisms of analyte desolvation in the ejected plume are discussed. Analyte fragmentation is found to be negligible under all explored conditions.