| Summary: | In order to analyze the stability of gravity–capillary short-crested waves propagating at the interface of two fluids of infinite depths, a numerical procedure has been developed using a collocation method. The three-dimensional wave is generated by an oblique reflection of a uniform wave train arriving at a vertical wall at some angle of incidence ${\theta }$ measured from the perpendicular to the wall. Fixing the reflection at angle $\theta =45\text{°}$, and wave steepness at $h=0.25$, we studied the influence of the density ratio $\mu $ and the inverse Bond number $\delta $ on the unstable area and the growth rate. It was observed that the unstable regions and the maximum growth rate decrease when $\mu $ and $\delta $ increase. Also, we found that the dominant instability belongs to the Class Ib as in the case of free-surface gravity waves in deep water.
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