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Based on the full-wave formulations, which combine the finite element method add the boundary element technique, and the step-like approximation method, a three-dimensional (3-D) electromagnetic modeling approach is proposed in this work to investigate the fiber-core effects on the coupling characteristics of the weakly fused tapered couplers. We find the fiber cores have significant effects on the mode field patterns, coupling coefficients, and birefringence for the coupler with large normalized frequencies. The influence of the fiber cores on the coupling behavior for the real couplers, such as 3 dB power dividers, polarization beam splitters, and wavelength demultiplexing/multiplexing couplers, are also studied in 3-D view. It is found that the effects of fiber-cores in the weakly fused tapered couplers have to be considered for accurately modelling their coupling behavior, although the model with no core assumption can predict the trend of the coupling characteristics for the real couplers.