The edge-related mechanical properties of fluorographene nanoribbons are investigated by means of first-principles calculations. It is found that for the four selected types of ribbons, edge energy quickly reaches a plateau when the width of ribbons exceeds 10 Å and then slowly increases at a rather small rate. Compressive and tensile edge stresses are found in ribbons with armchair and zigzag edges, respectively. The edge stresses are width dependent and also evidently smaller than those of graphene nanoribbons. This is understood to be due to the thickness effect of the two-dimensional (2D) layer structure of fluorographene. The in-plane stiffness and residual strains are also obtained for the selected fluorographene nanoribbons. The calculated in-plane stiffness gradually decreases as the ribbon width increases and approaches the counterpart of bulky fluorographene. Tensile and compressive residual strains led to armchair- and zigzag-edged fluorographene nanoribbons due to their different edge stresses, and both of them approach vanishing as the width increases since a larger width is equivalent to a larger stretch stiffness.