A theoretical modeling is presented for the laser pulse heating process in cylindrical twodimensional materials. The laser beam irradiates a local rounded regional strip of the surface and the exposed laser energy is absorbed by the surface. The governing energy equation is due to the Fourier heat conduction law with the laser heat source term incorporated. Making the energy equation non-dimensional leads to three main physical parameters together with three more auxiliary parameters. The dimensionless equation with these parameters are then solved analytically by means of integral transformations suitable to the problem geometry donated with proper insulated boundary constraints in combination with a uniform initial temperature condition. The present model is validated by comparing it with the dimensional counterparts available in the open literature. The rigorous convergent solutions are shown with and without the initial temperature. Through a detailed parametric analysis, the effects of laser irradiation on the material energy absorption of the laser energy, on the temperature rise of the surface, on the heat distribution through the material penetration, and on the radial and temporal laserbeam/material interaction time bandwidth are easily understood from the presented model and analytical solutions.