This paper presents a method of estimation of the nominal ocular hazard distance (NOHD) and the nominal ocular dazzle distance (NODD) for multibeam laser radiation. For the analysis, laser beams propagating in the same optical path (overlapping) but with different wavelength, power, and divergences in two perpendicular planes were assumed. To the authors' best knowledge, such a comprehensive analysis of multiple beams, considering the above parameters, is being presented for the first time. The dazzling possibilities described thus far assumed a single beam of radiation with a circular cross-section. This article also presents the calculation results of the NOHD and the NODD values for three laser beams with wavelengths in the red, green, and blue radiation spectrum with assumed parameters. Similar calculations were also made for a commercial laser source with potential use for laser dazzling. The presented analysis did not take into account the attenuation of radiation by the atmosphere. Moreover, the study provides recommendations on how to design effective, but safe, multiwavelength laser dazzlers.