Аннотация:In this paper, the problem of continuation of the solution of the ill-posed Cauchy problem for matrix factorizations of the Helmholtz equation in a two-dimensional bounded domain is studied. It is assumed that the solution to the problem exists and is continuously differentiable in a closed domain with exactly given Cauchy data. For this case, an explicit formula for the continuation of the solution is established, as well as a regularization formula for the case when, under the indicated conditions, instead of the Cauchy data, their continuous approximations with a given error in the uniform metric are given. A stability estimate for the solution of the Cauchy problem in the classical sense is obtained.