We report measurements of the in-plane magnetoelastic coupling in both as-deposited and annealed ultrathin Ta/CoFeB/MgO layers as a function of uniaxial strain, conducted using a four-point bending apparatus. While as-deposited samples show only a weak dependence of the magnetoelastic coupling on the CoFeB layer thickness in the ultrathin regime (<2nm), we observe the onset of a strong thickness dependence upon annealing. This dependence can be modeled as arising from a combination of effective surface and volume contributions to the magnetoelastic coupling. We point out that if similar thickness dependence exists for magnetoelastic coupling in response to biaxial strain, then the standard Néel model for the magnetic anisotropy energy acquires a term inversely proportional to the magnetic layer thickness. This contribution can significantly change the overall magnetic anisotropy, and provides a natural explanation for the strongly nonlinear dependence of magnetic anisotropy energy on magnetic layer thickness that is commonly observed for ultrathin annealed CoFeB/MgO films with perpendicular magnetic anisotropy. © 2016 American Physical Society.