The Hubble Space Telescope (ST) will be launched with five dedicated scientific instruments and a capability to do astrometric measurements with the fine guidance sensors. Four of these – the Faint Object Camera, the Wide Field Camera, the Fine Guidance Sensors and the High Speed Photometer – can be used in the search for extrasolar planetary systems. The Faint Object Camera will be able to directly detect planets around a few of the nearby bright stars. The Wide Field Camera and the Fine Guidance Sensors can be used astrometrically, both with an accuracy of about 2 mas per observation. The High Speed Photometer possibly can detect planets during occultation of stars by the moon and minor planets. The ST is expected to be launched in mid-1986 and these observations are the among the first planned with the instruments.