Islands and critical thickness of InAs grown by molecular beam epitaxy are investigated. The InAs layers are grown on. the (001) nominally- and misoriented GaAs substrates at 480 degrees C. They are characterized with atomic force microscopy and transmission electron microscopy observations and photoluminescence measurement. The InAs grows two-dimensionally at first and then begins the transition to three-dimensional growth, i.e., island formation at 1.8 mono-molecular layers (ML), The island size is not varied much, but follows a Gaussian distribution centred at 13-15 nm. We demonstrate, by observing polarized photoluminescence, that the islands can be utilized as a mesoscopic structure which has been proposed, The observations show that the critical thickness of InAs grown on the nominally-oriented substrate is 3 ML. The thickness can be increased to 5 ML with the growth on the substrate misoriented to the [1(1) over bar0$] direction by 3.5-5.0 degrees, The critical thickness is theoretically studied taking account of the strain energy calculated by the valence-force field method, The theory interprets well the experimental results.