Interest to Fiber concrete - concrete reinforced with short randomly distributed in the material volume fibers is growing and obtaining more new fields of application. Initially used fibers were steel. Composite Fibers (CF) have become competitive with steel fibers, fiber concretes with such fibers are now under investigation. In the present research, authors investigated the bond strength between the fiber and concrete, as well as other mechanical characteristics of the fiber concrete with CF. CF were made of short basalt micro-fibers glued together by Epoxy resin. Basalt micro-fiber roving (250 filaments) was taken as a main source of the CF, it was impregnated with epoxy resin. The Epoxy resin to hardener ratio was 3:1. After a few days maturing prepared CF were cut down into short fibers of a size of 24 mm. The authors planned to prepare concrete samples for the single fiber pull-out test and composite fiber-reinforced concrete prisms for the four-point bending test. Another product used in the investigation was Oil Shale Ash (OSA). OSA is a class-C fly ash. OSA was used as a partial cement replacement in a concrete. The concrete mixture was prepared with different compositions in addition to Oil Shale Ash (was used OSA from Auvere, Estonia, thermal power plant) as replacement of cement in ratios of 0%, 10%, 20%, and 30%. Tests were performed to obtain the load-bearing capacity of a concrete with basalt fibers. An important property of every kind of fiber is the single fiber behavior under pull-out conditions. Microscopic analysis has been made to conclude the research.