The elastic stress and strain fields in a circular cross-section bar with semielliptic groove subjected to uniaxial tension are systematically investigated using the finite element method. It is found that the stress and strain concentrations are different even if the material is in the elastic state. The relation between the stress and the strain concentration factors depends on Poisson’s ratio and the groove’s geometric configuration. The coupled influences of the shape factor of the semielliptic groove and the relative depth of the groove on the stress and strain concentrations are examined. The equations that describe the stress and strain concentration factors for different groove’s geometric configurations and Poisson’s ratios are obtained based on finite element results.