The problem of radar constant-modulus (CM) waveform design for the detection of multiple targets is considered in this paper. The CM constraint is imposed from the perspective of hardware realization and full utilization of the transmitter's power. Two types of CM waveforms — the arbitrary-phase waveform and the quadrature phase shift keying waveform — are obtained by maximizing the minimum of the signal-to-clutter-plus-noise ratios of the various targets. Numerical results show that the designed CM waveforms perform satisfactorily, even when compared with their counterparts without constraints on the peak-to-average ratio.