The Goos-Hanchen effect, a longitudinal shift of a wave beam at total inner reflection, is a well-known optical phenomenon. It was discovered in 1947 and have been observed many times at reflection of micro- and ultrasonic waves since then. Here we present an elementary theory of the GH. effect to describe reflection of a massive particle and demonstrate how the shift is related to delay time at reflection. It is shown that giant positive or negative longitudinal shifts of the neutron beam may occur at neutron reflection from some specially manufactured planar system. The possibility of delay time measurement at neutron reflection and direct experimental observation of the GH shift are also discussed.