The effectiveness of Fibre-Reinforced Polymer (FRP) and Textile-Reinforced Mortar (TRM) jackets was investigated experimentally and analytically in this study as a means of confining old-type reinforced concrete (RC) columns with limited capacity due to bond failure at lap splice regions. The local bond strength between lap spliced bars and concrete was measured experimentally along the lap splice region of six full-scale RC columns subjected to cyclic uniaxial flexure under constant axial load. The bond strength of two column specimens tested without retrofitting was found to be in good agreement with the predictions given by two existing bond models. These models were modified to account for the contribution of composite material jacketing to the bond resistance between lap spliced bars and concrete. The effectiveness of FRP and TRM jackets against splitting at lap splices was quantified as a function of jacket properties and geometry as well as in terms of the jacket effective strain, which was found to depend on the ratio of lap splice length to bar diameter. Consequently, simple equations for calculating the bond strength of lap splices in members confined with composite materials (FRP or TRM) are proposed.