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Thin-walled structures are of much interest as energy absorption devices for their great crashworthiness and also low weight. Conical tubes are favorable structures because unlike most other geometries, they are also useful in oblique impacts. This paper investigated the effect of corrugations on energy absorption characteristics of conical tubes under quasi-static axial and oblique loadings. To do so, conical tubes with different corrugation geometries were analyzed using the finite element explicit code and the effects of corrugations on initial peak crushing force and specific energy absorption were studied. The finite element model was validated by experimental quasi-static compression tests on simple and corrugated aluminum cylinders. An efficient analytical solution for EA during axial loading was also derived and compared with the FEM solution. The crushing stableness was analyzed using the undulation of the load-carrying capacity parameter and it was shown that corrugations made collapsing mode, more predictable and controllable. The findings have shown that corrugated conical tubes have much better energy absorption characteristics compared with their non-corrugated counterparts. It was also discovered that during oblique loadings, introducing corrugations can significantly increase the specific energy absorption compared with simple cones.