Acoustic logging while drilling (LWD) is an important commercial technology for oil and gas exploration. However, the collar wave in the full waveform has been found to interfere with signals from the formation, making it difficult to obtain formation compressional and shear velocities from acoustic LWD signals. We investigated seismoelectric LWD to solve this problem. We focused on the feasibility of obtaining the formation acoustic compressional and shear velocities from electric signals that go with acoustic waves near the borehole due to the electrokinetic effect. The theoretical full waveform of the seismoelectric LWD was simulated by one-way conversion approximation. The full waveform of acoustic pressure was simulated first, with a viscoelastic formation medium. The pore pressure was then estimated by confining pressure. The electric field excited by the elastic wave was seen as quasistatic and was simulated by solving the Poisson equation under the borehole conditions with an inhomogeneous term generated by the acoustic disturbance. In the full waveform of the synthesized electric field, there was a signal traveling with the collar wave speed, as well as signals accompanying compressional, shear, and similar guided wave groups. The converted electric collar wave signal was weaker than its acoustic counterpart, in terms of their amplitudes relative to other wave groups in their respective full waveforms.