Abstract The material removal mechanism in cutting of carbon fiber reinforced polymer (CFRP) varies with fiber orientation and tool rake angle due to its two-constituent structure. When the fiber orientation is zero degree and tool rake angle is zero or negative, the chip formation process is dominated by the shearing at the interface layer and the buckling of uncut workpiece material. This paper develops a new analytical mechanics model of orthogonal cutting of unidirectional CFRP to predict the forces and chip lengths with shearing-buckling deformation mechanism of the material. A shearing model is developed to determine the maximum resistance force of the workpiece material using energy method. The lengths of machined chips are evaluated based on micro and Euler buckling theories. The tool-workpiece contact force due to tool pressing at the cutting tool edge and flank face is predicted. The developed model reveals the nonlinear relationship between the cutting force and the uncut chip thickness in orthogonal cutting of CFRP. The simulated cutting forces and chip lengths are verified by experimental results at different uncut chip thicknesses and tool rake angles. The developed model determines the fundamental mechanism in orthogonal cutting of CFRP due to its unique anisotropic property.