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Abstract Despite extensive modeling efforts, the dynamics of subduction initiation (SI), including the role of elasticity, are not fully understood. Using two‐dimensional thermomechanical models with visco‐plastic (VP) and visco‐elasto‐plastic (VEP) rheologies, we systematically investigate the role of elasticity in intraoceanic SI using two model setups: spontaneous initiation without imposed convergence and induced initiation with imposed convergence. In spontaneous models, the overriding plate age of <20 Ma and the subducting plate age of >50 Ma generally lead to vertically driven SI with either rheology, but for a given age contrast, SI is easier to occur with the VEP rheology. In induced model with either rheology, when the two plates are young and have a small age contrast, the resulting SI is horizontally driven, and elasticity does not affect SI significantly, regardless of the convergence rate. However, when the thermal age contrast is large and a convergence rate is relatively low, the SI in induced models is vertically driven and similar to that in the spontaneous models, and the VEP rheology leads to faster SI than the VP rheology. This effect of elasticity becomes smaller with increasing initial horizontal compressional stress but does not become fully negated by the initial stress of <∼50 MPa. Therefore, inclusion of elasticity with reasonable shear modulus and initial stress values results in a weaker slab, making it easier for vertically driven SI to occur when the age contrast is relatively large.