Simplified one-dimensional field equations describing the clynamic deflections of a notched beam are developed using an elastodynamic variational principle, and solved approximately by the normal mode technique. The assumptions involved in the approximate solution are investigated in detail, and are shown to be justified with the aid of some recently obtained results concerning the stability of notched columns. NOTATION a notch depth A, cross sectional area of gross section b beam thickness E Young's Modulus F applied load (concentrated at midspan) f#~ mode I fraction toughness h beam half-height H Heaviside unit step function I, moment of inertia of gross section Kt mode ! stress intensity factor gt elastic stress concentration factor L beam length M bending moment P applied compressive load in the stability analysis p applied load per unit length on the top surface of the beam R notch root radius u, displacement vector V shear force Yi (x) eigenvector of the beam field equations d measure of the influence of the local stress field of the notch 8 Dirac delta function eccentricity /z shear modulus zo stress tensor p mass density o~, eigenvalues of the beam field equations (natural frequencies).