Within the rapidly growing market for fiber-reinforced plastics (FRPs), conventional production processes involving molds are not cost-efficient for prototype and small series production. Therefore, new flexible forming techniques are increasingly being researched, many of which have been inspired by incremental sheet metal forming (ISF). Due to the different deformation mechanisms of woven reinforcement fibers and metal sheets, ISF is not directly applicable to FRP. Instead, shear and bending of the fibers need to be realized. Therefore, a new dieless forming process for the production of FRP supported by metal wire mesh as an auxiliary material is proposed. Two standard tools, such as hemispherical punches, are used to locally bend a reversible layup of metal wire mesh and woven reinforcement fiber fabric enclosed in a vacuum bag. Therefore, the mesh aids in introducing shear into the material due to its ability to transmit compressive in-plane forces, and it ensures that the otherwise flexible fabric maintains the intended deformation until the part is cured or solidified. Basic experiments are conducted using thermoset prepreg, woven commingled yarn fabric, and thermoplastic organo sheets, proving the feasibility of the approach.