It is well known that radiation pattern A(($) over cap x, ($) over cap e) related to the scalar wave u(s)(x, ($) over cap e) scattered by a bounded body D, located in an infinite simple (homogeneous, isotropic, linear, local, time-invariant) space and illuminated by a monochromatic plane wave propagating in the direction of the unit vector ($) over cap e, satisfies the reciprocity relation A(($) over cap e', ($) over cap e) = A(-($) over cap e, -($) over cap e') and interrelates the outgoing and incoming wave solutions through a functional equation of the form u(x, ($) over cap e, omega) = integral[delta(($) over cap e - ($) over cap e') - (2 pi i)(-1)A(($) over cap e, ($) over cap e')]u(x, ($) over cap e', -omega)d ($) over cap e'. These concepts and relations play very important roles in investigations of direct as well as inverse scattering problems in simple spaces. In connection with some rather complicated configurations related to buried objects one has to know if these concepts and relations can be extended to the cases where the infinite region outside D is not homogeneous. The answer seems, in general, to be negative. In this paper it is shown that if D is a cylindrical body buried in a simple slab and A(($) over cap x, ($) over cap e) is properly normalized, then the pattern concept and reciprocity relation are still valid in a certain wedge-shaped region W-delta while a generalization of the relation u(x, ($) over cap e, omega) = Su(x, ($) over cap e', -omega) can be made in all the space. The half spaces above and below the slab are supposed to be filled with different simple materials. This configuration involves also the case of bodies buried in a half space as a particular case where the material of the slab and that of the region below it are identical.