An assumed displacement hybrid finite-element procedure developed for treating a general class of problems involving mixed-mode behavior of cracks is used to solve some two-dimensional, fracture mechanics problems involving rectilinear-anisotropic materials. This finite-element program uses four “singular” elements which surround the crack tip and “regular” elements which occupy the remaining region. The singular element has a built-in displacement field of the √r type with the two modes of stress intensity factors, K_I and K_II, as unknowns. Displacement compatibility between singular and regular elements is also maintained. Isoparametric transformations are used to derive the stiffness matrix of quadrilateral curved elements. Rectilinear anisotropic, nonhomogeneous, but linear elastic, material properties are considered. The program was checked out by analyzing a bimaterial tension plate with an eccentric crack and a centrally-cracked orthotropic tension plate. The results thus obtained agreed well with those by Erdogan and Biricikoglu, and Bowie and Freese, respectively. The program was then used to analyze two fracture test specimens for which analytical solutions do not exist. The first specimen was the doubly edge-notched tension plate with material principal directions oriented 0°–90° or ±45° to the geometric axes of symmetry and with varying crack length. The second specimen was the three-point bend specimen with material principal directions oriented 0°–90° to the geometric axes of symmetry. Finally, an orthotropic tension plate with an oblique center crack was analyzed. Finite-element solutions of most of these problems do not seem to have appeared in prior literature.