We consider a problem of approximation by entire functions of exponential type of functions defined on a countable set E of continuums G_n, E = E =⋃_(n∈Z)Gn. We assume that all G_n are pairwise disjoint and are situated near the real axis. We assume too that all G_n are commensurable in a sense and have uniformly smooth boundaries. A function f is defined independantly on each Gn and is bounded on E and f ^(r) has a module of continuity ω which satisfies a condition ∫_0^x▒〖ω(t)/〗 t ∙ dt + x ∫_x^∞▒〖ω(t)/t2〗 ∙ dt ≤ cω(x). Then we construct an entire function Fσ of exponential type ≤ σ such that we have the following estimate of approximation of the function f by functions F_σ : |f (z) - F_σ (z)| ≤ c_f σ^-rω(σ^-r ), z ∈ Z, σ ≥ 1.