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3D Gaussian Splatting (3DGS) has emerged as a leading representation for real-time novel view synthesis and been widely adopted in various downstream applications. The core strength of 3DGS lies in its efficient kernel-based scene representation, where Gaussian primitives provide favorable mathematical and computational properties. However, under a finite primitive budget, the symmetric shape of each primitive directly affects representation compactness, especially near asymmetric structures such as object boundaries and one-sided surfaces. Recent works have explored more complex kernel distributions, yet they either remain within the elliptical family or rely on hard truncation, which limits continuous shape control and introduces distributional discontinuities. In this paper, we propose Skew-Normal Splatting (SNS), which adopts the Azzalini Skew-Normal distribution as the fundamental primitive. By introducing a learnable and bounded skewness parameter, SNS can continuously interpolate between symmetric Gaussians and Half-Gaussian-like shapes, enabling flexible modeling of both sharp boundaries and interior regions. Moremover, SNS preserves analytical tractability under affine transformations and marginalization. This property allows seamless integration into existing Gaussian Splatting rasterization this http URL, to address the strong coupling between scale, rotation, and skewness parameters, we introduce a decoupled parameterization and a block-wise optimization strategy to enhance training stability and accuracy. Extensive experiments on standard novel-view synthesis benchmarks show that SNS consistently improves reconstruction quality over Gaussian and recent non-Gaussian kernels, with clearer benefits on sharp boundaries and thin or one-sided structures.