Ophiolite obduction, the process during which part of the oceanic crust overlaps the continental margin, presents a challenge in geodynamic reconstructions of lithospheric processes. The difference in buoyancy between the dense oceanic crust and the relatively buoyant continental crust makes obduction of the oceanic crust difficult, if not impossible, if we only consider the buoyancy forces. The initial configuration of the oceanic basins must have specific thermal and geometric constraints to overcome the difficulties posed by the negative buoyancy. Here, we present a systematic investigation of the geometric and geodynamic parameters controlling the process of ophiolite emplacement. We show which parameters are the most important during ophiolite emplacement and the optimum geometries favouring this emplacement. We focus on ‘Tethyan’ ophiolites, which are characterized by a relatively small inferred basin size and are commonly found in the Mediterranean region. Based on a combination of parameters, we identify the configurations most susceptible to ophiolite obduction. Our models, in agreement with the geological data, show that to achieve ophiolite obduction, the obducted lithosphere must be young and the length of the ocean–continent transition zone must be relatively sharp. Supplementary material: Supplementary figures S1–S5, that are mentioned in the main text, are available at https://doi.org/10.6084/m9.figshare.c.6922526 Thematic collection: This article is part of the Ophiolites, melanges and blueschists collection available at: https://www.lyellcollection.org/topic/collections/ophiolites-melanges-and-blueschists