In the field of dental study it is most fundamental and necessary to estimate the condition of periodontium. In order to examine a mechanical characteristics of periodontium, the theoretical displacement response to periodontal mechanical model (three elements model) are strictly solved in case of some pulse excitations. Impact excitations (rectangular, triangular and half-cycle sine pulse) are given in physical and mathematical definitions and complete solutions to the impact excitations are provided. The triangular pulse excitation which is obtained by means of a fracture of pencil-lead is most suitable. The mechanical parameters of periodontium are given using this input excitation. This is experimentally confirmed by artificial tooth model. The obtained mechanical characteristic of the periodontal tissues can be applied to clinical diagnosis.