ACCORDING TO THE HISTORY OF ELASTIC'S MANIPULATORS, SOME PROBLEMS WITH A DESIGN AND A CONTROL OF THE ELASTIC'S MANIPULATOR ELEPHANT'S TRUNK TYPE ARE INTRODUCED. WE PROPOSE OUR OWN STRUCTURE OF THE MANIPULATOR. THE DESIGN OF OUR MODEL IS DESCRIBED IN THE PAPER. THE PHYSICAL MODEL, THAT WAS DESIGNED USING THE FINITE ELEMENT'S METHOD, IS PRESENTED. ALSO PRESENTED ARE MATHEMATICAL ASPECTS OF THE MODEL DESIGNS. WE INTRODUCE EXAMPLES OF ISSUES OF COMPUTER'S ANALYSIS.