Drag-based editing allows precise object manipulation through point-based control, offering user convenience. However, current methods often suffer from a geometric inconsistency problem by focusing exclusively on matching user-defined points, neglecting the broader geometry and leading to artifacts or unstable edits. We propose FlowDrag, which leverages geometric information for more accurate and coherent transformations. Our approach constructs a 3D mesh from the image, using an energy function to guide mesh deformation based on user-defined drag points. The resulting mesh displacements are projected into 2D and incorporated into a UNet denoising process, enabling precise handle-to-target point alignment while preserving structural integrity. Additionally, existing drag-editing benchmarks provide no ground truth, making it difficult to assess how accurately the edits match the intended transformations. To address this, we present VFD (VidFrameDrag) benchmark dataset, which provides ground-truth frames using consecutive shots in a video dataset. FlowDrag outperforms existing drag-based editing methods on both VFD Bench and DragBench.