This paper describes a general analysis of the vibration characteristics of thin, open, conical isotropic panels using the h-p version of the finite element method in conjunction with Love's thin shell equations. The convergence properties of this element have been established for particular geometries, thereby endorsing its suitability for use in further parameter studies. Natural frequencies and modes have been obtained for two completely free panels using (i) the h-p methodology reported here, (ii) a commercially available finite element package, and (iii) experimental work. Excellent agreement has been found between all three approaches. Some further comparisons with the work of other investigators have also been performed, and generally good agreement has been found. Finally, a brief parameter study has been presented for clamped and simply supported open conical panels with an included angle of p/3, whose semi-vertex angle has been varied continuously between 0 and p/2. It is noted that the methodology advanced here for a generic conical panel can also be used to analyse the dynamic behaviour of closed conical frusta, open or closed cylindrical shells, and flat annular sectorial plates.