  We discuss possibility to obtain stronger constraints on non-Newtonian
gravity from measuring the gradient of the Casimir force between a cylinder and
a plate. Exact analytical expression for the Yukawa-type force in a
cylinder-plate configuration is obtained, as well as its asymptotic expansions.
The gravitational force is compared with the Casimir force acting between a
cylinder and a plate. Numerical computations for the prospective constraints on
non-Newtonian gravity are performed for recently proposed experiment using a
microfabricated cylinder attached to a micromachined oscillator. Specifically,
it is shown that this experiment is expected to obtain up to 70 times stronger
constraints on the Yukawa-type force, compared with the best present day
limits, over a wide interaction range from 12.5 to 630 nm.
