Mathematical dependencies for calculation of main parameters of vacuum gripping devices have been derived with the purpose of increasing efficiency of devices developed for handling of flexible containers during filling with free-flowing products. Computer modelling of the process of gripping and holding of flexible containers made with air-penetrating materials with the help of vacuum gripping devices of various types and sizes has been completed. Experimental research of precision of positioning of pneumatic cylinder rod with vacuum gripping device has been conducted, as well as the probability and reliability of gripping, transporting and opening of flexible containers. Achieved results confirm possibility of using vacuum gripping devices for automated handling of flexible air-penetrating container when it is filled with free-flowing products.