The present study deals with LRS Bianchi type I cosmological model representing massive string. The energy-momentum tensor for such string as formulated by Letelier (1983) is used to construct massive string cosmological models for which we assume that the shear scalar ($\sigma$) is proportional to the expansion scalar ($\theta$). The study reveals that massive strings dominate the early Universe. The strings eventually disappear from the Universe for sufficiently large time, which is in agreement with the current astronomical observations. Some physical and geometrical behaviour of models are also discussed.