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The non-destructive evaluation of elastic and poroelastic materials plays a vital role in various branches of engineering, such as material science, the petroleum industry, soil mechanics, geophysics, and biomechanics. Over the past few decades, Guided Wave (GW) technologies have emerged as effective tools for Structural Health Monitoring and Nondestructive Evaluation. These technologies exhibit sensitivity to both material and structural properties. The accurate assessment of materials and structures using GW testing techniques relies on understanding wave dispersion characteristics. When analyzing complex geometries of coupled fluid-solid waveguides, the semi-analytical finite element (SAFE) method often requires extensive computational efforts, particularly at high-frequency ranges. In this study, we demonstrate the effectiveness of a robust computational approach known as semi-analytical isogeometric analysis (SAIGA) in calculating wave dispersion in 3D anisotropic elastic or poroelastic waveguides coupled with fluids. The SAIGA approach employs Non-Uniform Rational B-splines (NURBS) as basis functions for geometry representation and the approximation of pressure/displacement fields. We compare the results obtained from SAIGA with those derived from the conventional SAFE method that utilizes Lagrange polynomials. Our findings reveal that SAIGA exhibits significantly faster convergence rates in computing the dispersion of GWs compared to the conventional SAFE method, even when using the same order of shape functions. For hollow prismatic structures immersed in fluids, employing high-order NURBS (e.g., p=8) proves particularly efficient, as it requires only a few elements to achieve results of the same precision as those obtained by SAFE, which demands up to five times the number of Degrees of Freedom (DoFs). Furthermore, the smoothness property of NURBS leads to significant improvement in the continuity of normal displacement at fluid-solid interfaces. This characteristic highlights the advantage of SAIGA over SAFE when evaluating the shape modes of GWs in coupled fluid-solid systems.