  Axion is a light pseudoscalar particle of much interest for physics of
elementary particles and for astrophysics. We review the recently obtained
constraints on axion to nucleon coupling constants following from different
experiments on measuring the Casimir interaction. These constraints are
compared with those following from other laboratory experiments within the wide
range of masses of axion-like particles from 10^{-10} to 20 eV. We also collect
the most strong constraints on the Yukawa-type and power-type corrections to
the Newton law of gravitation which follow from measurements of the Casimir
interaction, Eotvos- and Cavendish-type experiments. The possibility to obtain
stronger constraints on an axion from the Casimir effect is proposed.
