The effect of side grooves in standard compact tension (C(T)) specimens on the constraint due to plasticity under small scale yielding is presented in this paper. The Elastic-plastic crack-tip stress state is analysed through three dimensional finite element method. Ramberg-Osgood model is used to characterize the smooth transition of elastic-plastic behavior at the onset of crack-tip under Small Scale Yielding. Side grooves of type V and U are analysed and compared with plain specimen. Generally, it is observed that the plane stress effect on the surface of the plain specimen is restricted by the introduction of the side grooves. And this effect is studied with the in-plane crack-tip constraint parameter Q and out-of-plane constraint parameters Tz and h through the specimen thickness. It is found that localized plastic deformation at the side grooves increases the constraint level of the cracked specimen at the side grooves whereas it shows less at the middle of the specimen. It is also concluded that compared with U- groove specimen, V- groove specimen shows better constraint level. © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0)