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Rainfall-triggered shallow landslides are one of the most frequent geomorphological processes in tropical mountainous terrains, and they deserve special attention due to their potential negative consequences in society. Such processes involve several variables including those regarding precipitation, terrain morphology, and hydraulic and shear strength parameters of saturated and unsaturated soils. A spatially distributed and physically-based model for transient rainfall infiltration and grid-based regional slope stability analysis (TRIGRS), was implemented. It was used to analyze the influence of the mentioned variables on the triggering of shallow landslides by rainfall. A robust sensitivity analysis was carried out to quantify the influence of parameter variation on the change of the factor of safety ($$\Delta f_\textrm{s}$$ Δ f s ) for shallow landslides, including a one-parameter-at-a-time analysis of a unique cell representing the simplest model space. Four combinations of saturated/unsaturated models and finite/infinite infiltration models were analyzed. The interaction among the hydraulic parameters was analyzed through small-multiple plots to observe their influence on $$\Delta f_\textrm{s}$$ Δ f s . It was found that $$\Delta f_\textrm{s}$$ Δ f s is most sensitive to variation in the maximum depth at which the landslide can be triggered, the slope angle, the cohesion, and the friction angle. In addition, it was found that the parameters of the soil–water characteristic curve for unsaturated soils have little influence on $$\Delta f_\textrm{s}$$ Δ f s . Finally, the interactions among the remaining parameters determine the impact of each one of these on $$\Delta f_\textrm{s}$$ Δ f s . Thus, the results showed that when the baseline set of parameters is changed, the influence of each parameter is modified.