This article provides a detailed analysis of issues related to the complications while drilling in hydrate-bearing rocks of permafrost areas. The goal of the paper is to develop recommendations for preventing gas occurrence while drilling gas hydrate deposits and to eliminate gas leakiness of the intercasing space of the well. The results of modeling the effect of drilling mud injection on the temperature field of the well are presented. It is revealed that the most significant role is played by the injection rate of drilling mud and its temperature. The recommended flow rate of the process fluid should be within 0.30−0.45 m3/s, and its temperature should not exceed 20 °C. Controlling the parameters of drilling mud and its flow rate allows for avoiding intensive gas occurrence while drilling in gas hydrates. The presence of gas hydrates may be the cause of gas leakiness of the intercasing space in the permafrost area. One of the ways to eliminate leakiness is colmatation (clogging). A method of preventing leaks in the intercasing space of the gas well is the use of colmatating solution. An aqueous solution of sodium silicate with the addition of 2% polymer is used as a colmatating composition.