We have qualitatively analyzed, in the H and K lines spectral region, 31 flares covering part of umbrae or penumbrae of sunspots. A strong narrowing of the emission lines has been observed over the umbrae, and the lines are, in general, much weaker than in common flares suggesting that the optical thickness is quite low in these parts. We have calculated the Stark broadening of the He line from the general theory, and it has been applied to obtain the electron density in 9 flare spectra. In all cases it has been found that n~> 1013 cm -3. Goldberg's method has been applied to find the kinetic temperature from the H and K lines of Ca II, and from the ratio between the central intensities of the lines we have calculated the optical thickness in the K line. Much evidence supports the assumption that the flare emission is highly diluted* * in the cases considered, and we propose a two-component model for the calcium emission lines.