Let \(\Gamma\) be a set of a finite number of simple open curves in the plane. (A non-closed smooth arc of finite length without self-intersections is called simple open curve). \(\Gamma\) is considered as a set of cuts. The author considers the Helmholtz equation \(\Delta u+k^2u=0\) \((k=\text{const}\neq 0\), \(0\leq\arg k<\pi)\) in \(\mathbb{R}^2 \setminus\Gamma\) under jump boundary condition on \(\Gamma\) for the unknown function \(u\) and its normal derivative, satisfying appropriate conditions at infinity. The uniqueness of the solution in some class of functions is proved by the method of energy equalities. The solution of the problem is constructed as a sum of a single layer potential and an angular potential giving the uniquely solvable Fredholm integral equation of the second kind and index zero. Explicit formulas for singularities of the solution gradient at the ends of \(\Gamma\) are obtained as well.