  A bounded set $\Omega \subset \mathbb{R}^d$ is called a spectral set if the
space $L^2(\Omega)$ admits a complete orthogonal system of exponential
functions. We prove that a cylindric set $\Omega$ is spectral if and only if
its base is a spectral set. A similar characterization is obtained of the
cylindric sets which can tile the space by translations.
