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The paper is devoted to the study of the approximation properties of the biharmonic Poisson integral in the upper half-plane. The problem of approximating functions by biharmonic Poisson operators in the upper half-plane in the metric space L p (−∞, +∞) is considered. The main result of the paper is based on the representation of the integral kernel of the biharmonic Poisson integral obtained by applying the parameterization approach. It was found that the considered integral kernel belongs to the class of delta-shaped kernels. The upper bound is obtained for the approximation of functions by biharmonic Poisson operators in terms of the first-order modulus of continuity.