Micro-buckling characteristic of a carbon mono-fiber in matrix was studied. A fiber was modeled in matrix as a column on elastic foundation. Buckling stress of the fiber was calculated incorporating the initial fiber misalignment and non-linearity of the matrix. The effect of bending on compressive stress was also taken into considered to estimate failure initiation at fiber surface. Two processes of ultimate fiber failure were considered. First one is a compressive fracture at fiber surface due to compression and bending. Second one is a matrix-yielding initiated unstable fiber deformation. Compression test of a carbon fiber in matrix was performed by means of a four point bending test. Electrical resistance of the carbon fiber was measured during the compression test to recognize initiation of the compressive fracture. Fiber breaks at two adjacent locations were observed, which was caused by micro-buckling of the fiber. Apparent compressive strength of the fiber was measured in the experiment. Actual compressive strength of the fiber was predicted from the apparent compressive strength. Correlation between compressive strengths based on the elastic foundation model and the kink band model was discussed.