In the framework of the t-J model for cuprates we analyze the development of a pseudo gap in the density of states (DOS), which at low doping starts to emerge for temperatures T<J and persists up to the optimum doping. The analysis is based on numerical results for spectral functions obtained with the finite-temperature Lanczos method for finite two-dimensional clusters. We find that the pseudo gap scales with J and is robust also in the presence of nearest neighbor repulsive interaction. Numerical results are additionally compared with the self consistent Born approximation (SCBA) results for hole-like (photoemission) and electron-like (inverse photoemission) spectra at T=0. The analysis is suggesting that the origin of the pseudo gap is in short-range antiferromagnetic (AFM) spin correlations and strong asymmetry between the hole and electron spectra in the underdoped regime.