We show how to calculate the linear and nonlinear optical functions of CdSe nanoplatelets, taking into account the effect of a dielectric confinement on excitonic states. We consider both stationary and non-stationary excitation regime. We obtain obtain analytical expressions for the absorption coefficient, the exciton resonance energy and binding energy of nanoplatelets. The impact of plate geometry (thickness, lateral dimension) on the spectrum is discussed. In the nonlinear case we analyze the impact of temperature. For the short-pulse excitation the time dependence of the spectra is considered. The results are compared with the available experimental data.