In this paper, proper orthogonal decomposition (POD) is used for the first time to analyze weld pool surface dynamics during the laser beam welding (LBW) process. Despite the growing importance of laser beam welding in modern manufacturing, the mechanisms behind the formation of weld surface structures are not completely understood. Periodic structures in the weld bead and its surface can be observed even when welding with a continuous-wave laser along a linear path at constant welding speed and laser power. Therefore the present study proposes a novel approach to better understand the dynamics underlying such structures, using modal analysis to identify the dominant spatial modes within this highly dynamic system. The feasibility of the methodology for high-power laser beam welding is demonstrated by application to the velocity field calculated by a validated multiphysics numerical process simulation. The method is also applied to an experimentally obtained set of high-speed imaging data. For both the numerical and experimental data, dominant spatial modes are identified by POD analysis. A low-order model based on the most energetic modes with an axial wave structure is created. A spectral analysis of this low-order reconstruction is compared to a post-mortem surface scan and captures the same dominant frequency peak at around 2 Hz to 3 Hz. This finding suggests the dominant periodic rippling of the weld bead can be attributed to axial waves that originate from the keyhole. Modal analysis by POD is a promising approach for elucidating the phenomena associated with weld pool dynamics.