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A robust mathematical model is presented in this paper for the multi-connected domain with variable bathymetry using dual reciprocity boundary element method (DRBEM) to analyze the combined effects of wave diffraction-refraction and reflection on the arbitrarily shaped harbor. The influence of sloping bathymetry and the impact of the bottom friction on the harbor resonance are investigated. The fluid domain is primarily separated into two regions Region-I (open sea region) and Region-II (harbor region). Further, Region-II is divided into multi-connected regions. The mild slope equation is rearranged to obtain the non-homogeneous Helmholtz equation, and utilizing the ordinary boundary element method to this non-homogeneous equation, the non-homogeneous part will convert into a domain integral. The present model is verified by comparing it with the analytical examination of Wang et al.2015; Shao et al.2017. The wave amplification is determined for the T-shaped and TT-shaped domains to analyze the influence of bottom friction, and slopping bathymetry. Further, the present numerical approach is employed to the realistic port, Visakhapatnam port, India, and the four key locations are identified to analyze harbor resonance in the bottom friction and slopping bathymetry of the multi-connected region. • A Dual reciprocity boundary element method (DRBEM) with wave diffraction-refraction on the arbitrarily shaped harbor. • The influence of sloping bathymetry and effect of the bottom friction is also investigated. • Wave Amplification of the T-shaped and TT-shaped domains to analyze the influence of bottom friction, and bathymetry. • Implemented on the realistic Visakhapatnam port, Andhra Pradesh, India. • To analyze the harbor resonance on slopping bathymetry and effectively for redesigning, renovating and constructing ports. [ABSTRACT FROM AUTHOR]