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Purpose: The purpose of this study is to investigate the effects of the shear-thinning viscoelastic behavior of the surrounding matrix on droplet deformation by weakly compressible smoothed particle hydrodynamics (WC-SPH). Also, the effect of the presence of another droplet is examined. Design/methodology/approach: A modified consistent weakly compressible SPH method is proposed. After code verification, a complete parameter study is performed for a drop under the simple shear flow of a Giesekus liquid. The investigated parameters are 0.048≤Ca ≤ 14.4, 0.1≤c ≤ 10, 0.04≤De ≤ 10, 0≤α ≤ 1 and 0.12≤Re ≤ 12. Findings: It is demonstrated that the rheological behavior of the surrounding fluid could dramatically affect the droplet deformation. It is shown that the droplet deformation is increased by increasing Re and Ca. In contrast, the droplet deformation is decreased by increasing a, De and polymer content. Also, it is indicated the presence of another droplet could drastically affect the flow field, and the primary stress difference (N1) is resonated between two droplets. Originality/value: The main originality of this paper is to introduce a new consistent WC-SPH algorithm. The proposed method is very versatile for tackling the shear-thinning viscoelastic multiphase problems. Furthermore, a complete parameter study is performed for a drop under the simple shear flow of Giesekus liquid. Another novelty of the current paper is studying the effect of the presence of a second droplet. To the best of the authors' knowledge, this is performed for the first time. [ABSTRACT FROM AUTHOR]