The deformation of solid surfaces caused by the Laplace pressure is analyzed ad its effect on the meniscus force measurement is discussed by comparing it with the published experimental results of the meniscus force on a surface force apparatus. It is found theoretically that the deformation reaches the order of several nanometers and reduces greatly the meniscus force when the meniscus curvature radius is small. It is concluded that the deviation of the measured meniscus force with the surface force apparatus from equation F = 4 pi gamma R cos theta for a nanometer meniscus is due neither to the hydrogen bonding interaction (Fisher and Israelachvili, Colloids and Surf. 3, 303 (1981)) nor to the short range solid-solid interaction (Christenson, J. Colloid Interface Sci, 121, 170 (1988)). The main reason lies in the deformation of the solid surface due to the Laplace pressure. The nanometer deformation of solid surfaces caused by the Laplace pressure is of great importance in measuring the meniscus force.