Numerical experiments are used to investigate the thermo-mechanical 31 controls for inducing flat subduction and why flat subduction is rare relative to 32 normal/steep subduction. Our modeling results demonstrate that flat subduction is an 33 end-member of a steady state subduction geometry and is characterized by a curved 34 slab with a nearly-horizontal slab section. Intermediate cases between normal/steep 35 and flat subduction appear to be transient in origin and evolve toward one of the stable 36 end-members. Physical parameters inducing flat subduction can be classified into four 37 categories: buoyancy of the subducting oceanic lithosphere (e.g., slab age, oceanic 38 crustal thickness), viscous coupling between the overriding and downgoing plates 39 (e.g., initial subduction angle), external kinematic conditions, and rheological 40 properties of the subduction zone. On the basis of parameter sensitivity tests and the 41 main characteristics of present-day flat subduction zones, positive buoyancy from 42 either the young slab or the thickened oceanic crust are considered the primary 43 controlling parameter. Our results show that the possibility of flat subduction is 44 directly proportional to oceanic crustal thickness and inversely proportional to the slab 45 age. Furthermore, oceanic crust must be thicker than 8 km to induce flat subduction, 46 when the slab is older than 30 Ma with an initial subduction angle of ≥ 20°, and 47 49 likelihood for flat subduction. The initial subduction angle is more influential for the 50 development of flat subduction than the overriding lithospheric thickness, and a thick 51 overriding lithosphere induces flat subduction only under the condition of an initial 52 3 subduction angle of ≤ 25°, with a slab age of ≥ 30 Ma and without absolute 53 trenchward motion of the overriding plate. However, when the initial subduction 54 angle is increased to > 25°, no flat subduction is predicted. All the parameters are 55 evaluated within the constraints of a mechanical framework in which the slab 56 geometry is regarded as a result of a balance between the gravitational and 57 hydrodynamic torque. Any factor that can sufficiently reduce gravitational torque or 58 increase hydrodynamic torque will exert a strong effect on flat subduction 59 development. Our results are consistent with the observations of modern flat 60 subduction zones on Earth. 61 Keywords: flat subduction, numerical modeling, slab buoyancy, viscous interplate 62 coupling, external kinematic conditions 63 64 65 At convergent plate margins, variations in the dip of the downgoing slab of 66 oceanic lithosphere in its upper 125 kilometers enable the division of subduction 67 zones into low-angle (or flat) subduction (<30°), intermediate-angle subduction 68(between 30°-60°) and high-angle subduction (>60°) (e.g., Rodriguez-Gonzalez and 69 Negredo, 2012). As shown in Fig. 1, flat subduction, which is characterized by a 70 distinct flat-slab underlying the overriding lithosphere, occurs only in ~10 % of the 71 world's con...