Q-switched, solar-pumped, high power Nd:YAG lasers are attractive for a variety of applications requiring high instantaneous peak power density. The Q-switching can be obtained by an acousto-optic, electro-optic or passive device. Passive Q-switching seems an excellent choice for space as well as for other applications since it neither requires an external driver nor an electrical power supply. In recent years Cr+4:YAG single crystals were extensively used as passive Q-switches for flashlamp-pumped high power Nd:YAG lasers, demonstrating their superior thermal superior thermal characteristics and durability. In this work we report the first operation of passive Q- switched, solar-pumped, high power Nd:YAG lasers. The concentrated solar energy for he optical pumping of the laser was obtained by a 3-stage combination of imaging and non-imaging optics. It included: i) Weizmann Institute solar tower heliostats, ii) 3D compound parabolic concentrator, and iii) 2D compound parabolic concentrator in which the laser rod was placed. 72 mm long laser rods with either 3 mm or 4 mm diameter were used. The passive Q-switch was made from a Cr$=+4):YAG single crystal having a low- intensity transmission of 72 percent at 1.06 (mu) . Its rear surface was coated by a high reflectivity coating, serving as the rear mirror of the cavity. Output coupling mirrors with various reflectivities were used. The passive Q-switch demonstrated excellent durability and reliability during all the experiments. Repetition rates of 6-39 kHz were measured, showing higher repetition rates at higher laser power levels. The pulses demonstrated shorter full width at half maximum (FWHM) time for higher laser power elves, and the FWHM time range was 190-310 nsec. The maximal measured average power was 14 W. Thermal lensing was measured as a function of the absorbed solar power in the laser rod. It is estimated that laser peak power densities of approximately 100 kW/cm2 were achieved in the experiments. It is believed that near-future modifications may improve this value appreciably.