The requirement for accurate and efficient antenna design process is becoming more important with the advancement in technology and raised standards for electromagnetic compatibility. The accurate numerical solution of problems in electromagnetics ideally requires conformity of the mesh with the structure being modelled in order to attain this level of efficiency. Stability, ease of application and capability for wideband applications are some of the attributes that have made the Transmission Line Modelling (TLM) a versatile time domain, numerical modelling tool in solving electromagnetic problems. However, the parallelipedic nature of the Cartesian TLM model requires that curved boundaries are modelled with staircase approximations. Consequently, the efficient incorporation of these standard meshes in full-field time domain models for accurate description of curved boundaries is a challenge. This research describes the cylindrical TLM model procedure executed in MATLAB and its application to modelling of curvilinear radiating structures such as cylindrical and conical antennas. The significance of modelling cylindrical radiating structures with cylindrical TLM mesh is in the efficiency in time and computing resources management and better accuracy in the results obtained. The simulated results are in good agreement with the analytical expectations.