Oceanic-plates vertical tearing is seismically-identified in the present-day Earth. This type of plate tearing is frequently reported in horizontally-oblique subduction zones where transform-faulted oceanic plates are subducting (or subducted). However, the mechanisms behind vertical slab tearing are still poorly understood, thus we utilize 3D time-dependent Stokes’ flow thermo-mechanical models to further study this problem. We find that (i) the age offset of transform fault and (ii) the horizontal obliqueness of subduction fundamentally control the tearing behavior of two generic, materially-homogeneous oceanic slabs separated by a low-viscosity zone. The two slabs sequentially bend, which combined with the age-thickness difference between slabs, causes the differential sinking of them. Based on the modeling results, well-developed slabs vertical tearing would happen when the oblique angle of subduction is ≥30° or the age ratio of the secondly-bent to firstly-bent slab being ~<0.6. Quantifying the horizontal distance-vector between sinking slabs, we find that subduction at medium-low horizontal-obliqueness angles (≤40°) of young lithosphere (slabs-average ~15 Myr) tends to produce fault-perpendicular tearing. Contrastingly, old-age slabs (average ≥ 30 Myr) with medium-large obliqueness angles (~>20°) tend to produce fault-parallel tearing, related to differential slab-hinge retreat or rollback. Correlations between slabs’ (i) computed tearing horizontal-width and (ii) scaling-theory forms of their subduction-velocity differences, are reasonable (0.76-0.97). Our numerically-predicted scenarios are reasonably consistent with plate-tear imaging results from at least 4 natural subduction zones. Our modeling also suggests that continual along-trench variation in subduction dip angle may be related to a special case of oblique subduction.