Laser‐supported detonation waves have been studied with 15‐J 56‐MW/cm2laser pulses from a CO2Marx Bank laser. A smooth spatial and temporal laser beam profile was repeatable from pulse to pulse. Ignition thresholds for laser‐supported detonation waves were determined from relative reflected power and from framing camera photographs for many solid and liquid surfaces. Some of these thresholds were measured as functions of density of the medium (air) from 0.01 to 1 times atmospheric density. The velocities of laser‐supported detonation waves were studied to determine their dependence on laser beam intensity and medium density for conditions above the ignition thresholds of aluminum and lead surfaces. Streak camera photographs displayed clearly defined wavefronts whose initial velocities were constant until they were affected by decreasing laser beam intensities. When the temporal intensity changes in the beam and its focused geometry are included in calculations using the Raizer model for laser‐supported detonation waves to predict the wavefront motion, excellent agreement with the streak camera photographs was found. The initial velocity data are shown to agree with a power law in which velocity is proportional to (intensity/medium density)0.41±0.02. No explanation is proposed for the difference of the power law exponent from the 1/3 value predicted by the Raizer model.