Spectral Point Spread Function, or in other words Line Spread Function (LSF), quantifies a spectrograph's response to a monochromatic light source. Accurate knowledge of the LSF is needed to measure the velocity dispersion of the stars or gas from the spectra of galaxies, when these quantities are comparable or smaller than the width of the LSF. The LSF information is also crucial to subtract background sky emission in near-infrared integral field spectroscopic (IFS) instruments from ground-based telescopes. Accurate models of LSF cannot be obtained from the spectrograph data itself due to their coarse sampling to provide a wide instantaneous wavelength coverage. In the case of IFS instruments, the LSF can assume complex shapes and these shapes can change dependent on the location on the IFS field-of-view. In this manuscript, we derive accurate LSF models in the H-band grating of the SINFONI spectrograph, a near-infrared IFS on board the Very Large Telescope in Chile, using a dedicated calibration programme. We model the LSF profiles using Gauss-Hermite polynomials and we use the parameters from these models to predict the shape of the LSF profile at any location on the detector. We also demonstrate that the LSF can be derived from the curvature in the arc-lamp frames. Finally, we derive the LSF of the upcoming ELT/HARMONI spectrograph using the slit-curvature method for different resolutions and grating set-ups.