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• Construction of transparent boundary conditions (TBCs) for exural wave cavity scattering in two dimensions, ensuring the satisfaction of the sommerfeld radiation conditions. • Deduction of a decomposed problem for the biharmonic plate wave equation using two auxiliary functions and establishment of the unique-ness of the solution for the decomposed problem. • Proposal of the linear _nite element method with interior penalty term (IP-FEM) and boundary penalty term (BP-FEM) to solve the coupled boundary helmholtz and modi_ed helmholtz equations, leading to stable numerical solutions. • Introduction of an analytical solution for exural wave scattering by a circular cavity with a clamped boundary, facilitating comparative analysis. Flexural wave scattering plays a crucial role in optimizing and designing structures for various engineering applications. Mathematically, the flexural wave scattering problem on an infinite thin plate is described by a fourth-order plate wave equation on an unbounded domain, making it challenging to solve directly using the regular linear finite element method (FEM). In this paper, we propose two numerical methods, the interior penalty FEM (IP-FEM) and the boundary penalty FEM (BP-FEM) with a transparent boundary condition (TBC), to study flexural wave scattering by an arbitrary-shaped cavity on an infinite thin plate. Both methods decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary. A TBC is then constructed based on the analytical solutions of the Helmholtz and modified Helmholtz equations in the exterior domain, effectively truncating the unbounded domain into a bounded one. Using linear triangular elements, the IP-FEM and BP-FEM successfully suppress the oscillation of the bending moment of the solution on the cavity boundary, demonstrating superior stability and accuracy compared to the regular linear FEM when applied to this problem. [ABSTRACT FROM AUTHOR]