An approach for achieving line-structures in purely unstructured grids is presented in two-dimensions and three-dimensions. The method entails the identification of Hamiltonian paths created by quadrilateral subdivision of un-structured meshes to represent two distinct surface coordinate directions, and strand grids to represent the wall nor-mal direction. High-order stencil-based discretization and approximate factorization methods are used to construct line-implicit inversion operators along the loops and strands. Efficient solvers are then formulated that exploit these structures to the predict aerodynamic flow over bodies. Steady subsonic and transonic flow over an airfoil, wing, sphere and the Robin helicopter fuselage are predicted using the developed solver and compared against known results to validate the proposed methodology. Various mesh smoothing techniques and their effects on the solution conver-gence histories using multiple reconstruction schemes are explored. Domain decomposition techniques using message passing interface are developed to allow for the execution of the mesh generator and solver on parallel systems to contain the computational cost. Efficiency comparisons of the Hamiltonian solver against establish structured solvers are performed for representative cases and it is shown that the developed methodology achieves the convergence and accuracy of structured solvers. © 2015 Govindarajan, Jung, Baeder & Sitaraman.