The results of long-term contact measurements of the heights of short-period internal waves in the regions beside of the Solovki islands, of the southern border of Gorlo strait and to the North of the Kola Peninsula in the Barents Sea, made in the summer seasons of the years 2010 - 2016. The duration of measurements in each region was not less than 24 hours per season. It is established that for each day in each region, from 50 to 150 waves are observed, which on average have heights from 2 to 6 meters. In some of them, intense internal waves are recorded several times a day. The maximum recorded heights of internal waves in the White Sea are 18 meters, in the Barents Sea - 8 meters. Assuming the stationarity of the waveforming factors, estimates are made for the probability of occurrence of extreme heights of internal waves, which can be observed once a day, 10 days, 1 month, 2 months, 3 months. The most intense internal waves are expected in the White Sea, near the Western Solovki Strait, where once a month there will be waves up to 28 meters high, and waves more than 10 meters are expected in the area north of the Kola Peninsula, in the Barents Sea.