Abstract: On the basis of the introduction of the modified Cauchy kernel, this paper deals with the boundary value problem with Haseman shift for regular functions on unbounded domains:
a(t)Φ⁺(t)+b(t)Φ^-(d(t))+c(t)Φ^-(t)=g(t).
Firstly, the authors give the Plemelj formula functions on unbounded domains. Then, by the integral equation method and the fixed-point theorem, the authors prove the existence and uniqueness of the solution for the problem.

Key words: Real Clifford analysis, Regular function, Plemelj formula, Boundary value problem on unbounded domains, Integral equation.