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We discover a remarkable correlation between the inter-tremor time interval and the slenderness ratio of the overriding plate in subduction zones all over the world. In order to understand this phenomenon better, we perform numerical simulations of 3D deformation. The numerical buckling studies show that critical load and slenderness ratio indeed have an inverse nonlinear relation between them -- identical to the classical Euler's critical load relation, and closely resemble the relationship observed between the inter-tremor time interval and the slenderness ratio of the overriding plate. From the above analysis, we conclude that the observed relation is the result of buckling of the overriding continental plate. In addition to the above numerical analysis, we analyze the surficial 3D spatio-temporal displacements of the overriding plates in Cascadia and Alaska using 3-component GPS data. We find that these deformations are consistent with the buckling of the overriding continental crust. Based on these novel observations and guided by numerous existing scientific observations and findings, we propose an Episodic Buckling and Collapse model of subduction zones, wherein periodic geodetic changes and tectonic-tremor activity, result from the episodic buckling of the overriding continental crust and its rapid collapse on the subducting oceanic slab. According to this model, geodetic measurements, previously inferred as slow slip, are the surficial expressions of slowly-evolving buckling and rapid collapse of the overriding plate, while tremor swarms result from the striking of the collapsing overriding plate on the subducting slab (as opposed to slipping or shearing).