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This paper presents a finite element approach for determining the natural frequencies forplanar inclined arches of various shapes vibrating in three-dimensional space. The profile of inclinedarches, represented by undeformed centriodal axis of cross-section, is defined by the equation of planecurves expressed in the rectangular coordinates which are : circular, parabolic, sine, elliptic, and catenaryshapes. In free vibration state, the arch is slightly displaced from its undeformed position. The linearrelationship between curvature-torsion and axial strain is expressed in terms of the displacements in three-dimensional space. The finite element discretization along the span length is used rather than the total arclength. Numerical results for arches of various shapes are given and they are in good agreement withthose reported in literature. The natural frequency parameters and mode shapes are reported as functionsof two nondimensional parameters: the span to cord length ratio (e) and the rise to cord length ratio (f).