When drilling an oil well with a rotary drill, the penetration rate often can be substantially increased by superimposing a vibratory motion on the rotating bit. In order to evaluate drilling methods that would include both rotary and vibratory action, a study has been made on the vibrational characteristics of long drill string. The resonant frequency of a drill string consisting of a length of drill pipe and a length of drill collars is determined by considering the string as a lumped-constant system and also as an acoustic transmission line. A frequency equation is derived by applying the wave equation to the system and satisfying the boundary conditions at the top and bottom of the string and also at the junction of the two sections. The frequency equation is solved graphically for a number of drill-string configurations and the results are compared with the measured frequencies.