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The bending stress formula that taking into account the transverse deformation is developedfor plane-curved, untwisted isotropic beams subjected to loadings that result in deformations in the planeof curvature. In order to account the transverse Poisson contraction effect, a new constitutive relationstrains and deformed curvatures for a curved plateis derived in a 6 6 matrix form. This constitutive relation will provide the fundamental basis to theanalyses of curved structures composing of isotropic or anisotropic materials. Then, the bending stressformula of a curved isotropic beam can be deduced from this newly developed curved plate theory. Thestress predictions by the present analysis are compared to those by the analysis that neglected the Poisoncontraction effect. The results show that the Poisson effect becomes more significant as the Poisson ratioand the curvature are getting larger.