Laser-matter interaction in novel fusion welding technology of glass using ultrashort laser pulses is discussed, where the interface of glass plates is selectively melted for fusion welding by nonlinear processes without any absorbent, and crack-free welding can be obtained without pre- and post-heating. A semi-empirical model to describe laser-matter interaction model has been developed for evaluating the density distributions of the absorbed laser energy and free electrons, assuming that the free electron density at the beam waist reaches the critical value of 1021/cm3 at 1064nm, and that the laser energy absorbed by the free electron is totally converted into thermal energy. In this model, a simple line heat source model was introduced to evaluate the absorbed laser energy density distribution along the optical axis by fitting the calculated isothermal line to the experimental melt contour. Using thus obtained absorbed laser energy, an equation to calculate transient temperature distribution in the plasma column has been derived, assuming that laser spot size is given by Gaussian beam propagation equation. It was found that seed electrons for avalanche ionization is mainly provided by multiphoton ionization near the beam waist, and by thermal excitation at locations apart from the beam waist. Effects of different parameters on nonlinear absorptivity along with melt dimensions are also discussed at different parameters including pulse energy, pulse repetition rate, lens NA and translation speed. Welding characteristics are also discussed including development of weld cracks and the evaluation of joint strength.