For a pretwisted rod, in which torsional and flexural effects are decoupled, both vibration and buckling behaviour may be described by a pair of fourth-order linear ordinary differential equations. By considering the free vibration of axially-loaded pretwisted rods, a superset of the buckling and vibration equations may be obtained, and these equations may be solved analytically. Such solutions indicate that the relationship between the natural frequency and the applied load is effectively independent of the pretwist angle, for compressive loads and moderate tensile loads.NOTATIONA cross-sectional areac 1 , 8 real mode shape coefficientsE elastic modulusG shear modulusI 1 , 2 second moments of areak shear coefficientl rod lengthm 1 , 2 internal moment componentsq 1 , 2 internal force componentsP axial load (P > 0 compressive)P 0 buckling load of a prismatic rodP c r buckling load of a pretwisted rodr characteristic polynomial rootss normalized axial coordinate (= z/l)T total pretwist angle (= τl)u * 1 , 2 local displacement componentsu * 1 , 2 local displacement components associated with a root pairz axial coordinateθ * 1 , 2 local rotation componentsλ 2 dimensionless load parameter (= Pl 2 /EI 2 )μ bending stiffness ratio (= EI 1 /EI 2 )ρ mass densityτ twist per unit lengthΩ 4 dimensionless frequency parameter (= ω 2 ρAl 4 /EI 2 )ω natural frequencyω 0 natural frequency of an unloaded, prismatic rodω c r natural frequency of an unloaded, pretwisted rod