For the purpose of obtainning the approximate formulae of estimating the natural circular frequency a_n , the logarithmic decrement δ_n , and the amplitude A_n caused by the exciting force of known magnitude F, the author has carried out some investigations, the results of which are as follows. (1) a_n=√EI₀g (m⁴_n+X_n) /w₀l⁴ (1+Z_n) (1+r_n) (2) δ_n=πa_n {1/1+r_nα+r_n/1+r_nβ+1/a²_n (1+Z_n) (1+r_nγ)} (3) A_n=Fl³/EI₀πu_n (x) u_n (l₁) /δ_n (m⁴_n+X_n) The results of calculations by the use of these approximate formulae to the actual cargo ships on which the author had carried out the vibration tests by means of vibration exciter are compared with the data experimentally obtained, and it is shown that if the magnitude and the location of exciting force on board a vessel are given, it is possible to estimate not only the natural frequency but also the order of amplitude of her vibration.