The most successful numerical methods for solving hyperbolic conservation laws are found to be the Riemann solvers [1]. Such methods can also be applied to solid dynamics equations, when written them in the hyperbolic conservation law form. This has been the motivation here for developing a novel finite volume framework in formulating a Roe-type Riemann solver for a first-order system of solid dynamics equations. The conservative variables in this system include linear momentum and the deformation tensor[2]. The system of equations has been found to encompass all the essential properties required for the formulation of a Riemann solver, including hyperbolicity, homogeneity, and rotational invariance. One noteworthy aspect of the newly developed Roe-type solver is its remarkable simplicity of implementation in multidimensional problem and its possible extension to solve non-linear problems. Furthermore, the potential for solving both solid and fluid dynamics equations in a closely coupled manner for fluid-structure interaction problems becomes particularly promising when employing an identical numerical framework which is another motivation for the present work. This is another motivation behind developing the present solver for solid dynamics as the Roe solver already exists for the fluid dynamics equations. A few linear-elasticity test cases are solved and compared with the analytical solutions [3] in order to demonstrate the accuracy of the proposed solver. Cases include the pure shear stress deformation of a square plate and the bending of a cantilever beam under uniform load. Results are summarized in the table below: Test case | Mesh size | Numerical results | Analytical solution | Error %| Pure shear stress | 6x6 | 0.199 | 0.2 | 0.3| Beam bending | 80x8 | 0.296 | 0.3 | 1.3| REFERENCES [1] R.J. LeVeque, Finite volume methods for hyperbolic problems, Cambridge press, 2002. [2] C. H. Lee et al., Computers & Structures, Vol.118, pp. 13–38, 2013. [3] R.T. Fenner, Mechanics of Solids, John Wiley & Sons, Limited, 198