The problem of stress concentrations in the vicinity of pin-loaded holes is of particular importance in the design of multilayered composite structures made of triangular or circular glass fibers. It is assumed that all of the fibers in the laminate lie in one direction while loaded by a force p0 at infinity, parallel to the direction of the fibers. According to the shear lag model, equilibrium equations are derived for both types of fibers. A rectangular arrangement is postulated in either case. Upon the proper use of boundary and bondness conditions, stress fields are derived within the laminate, along with the surrounding pinhole. The analytical results are compared to those of the finite element values. A very good agreement is observed between the two methods. According to the results, composite structures made of triangular glass fibers result in lower values of stress concentrations around the pin, as opposed to those of circular glass fibers.