Quaternionic functions and their applications in mechanics of continua

Holomorphic functions are the key tool for solutions of two dimensional problems in mathematical and theoretical physics, mechanics of continua. For the three-dimensional problems the hypercomplex analysis is an analogical one, i.e. monogenic Clifford functions or regular quaternionic functions playing the role of a three-dimensional analogue of holomorphic functions. In this paper a survey of investigations in the quaternionic analysis have been made in the North-Eastern federal university (Yakutsk state university) from the 1980s is presented.