A basic solution in series form for the three-phase composite cylindrical model in antiplane piezoelectricity subjected to the action of a singularity in the intermediate matrix region is presented. The solution is obtained through the complex potential approach in conjunction with the techniques of analytical con tinuation, singularity analysis, Laurent series expansion in an annular region and Cauchy integral formulae,etc. Based on the complex potentials obtained, explicit expressions for the distribution of stress and electric displacement in the three regions are also derived.