Reconstructing three-dimensional (3D) structures from two-dimensional (2D) X-ray images is a valuable and efficient technique in medical applications that requires less radiation exposure than computed tomography scans. Recent approaches that use implicit neural representations have enabled the synthesis of novel views from sparse X-ray images. However, although image synthesis has improved the accuracy, the accuracy of surface shape estimation remains insufficient. Therefore, we propose a novel approach for reconstructing 3D scenes using a Neural Attenuation Surface (NeAS) that simultaneously captures the surface geometry and attenuation coefficient fields. NeAS incorporates a signed distance function (SDF), which defines the attenuation field and aids in extracting the 3D surface within the scene. We conducted experiments using simulated and authentic X-ray images, and the results demonstrated that NeAS could accurately extract 3D surfaces within a scene using only 2D X-ray images.