The titin springs of muscle sarcomeres largely determine tensile muscle stress. However, their anchorage at the Z-disk and A-band, respectively, means the titin springs are not strictly in parallel with the myofibrillar axis. On tensile strain, both longitudinal and radial force components arise. The radial component may increase A-band transversal stiffness, decrease lateral myofilament spacing, and determine length-dependent activation. We aimed to directly test by atomic force microscopy (AFM) whether the titin springs contribute to sarcomeric transversal stiffness and how a titin-based lateral force component would compare with other possible sources of lateral stiffness. Single myofibrils were isolated from rabbit psoas (stiff titin-isoform) or diaphragm (compliant titin-isoform) muscles and placed in physiological buffer under the MFP-3D-BIO AFM (Asylum Research). Force curves (50x50) were performed over a region-of-interest encompassing a whole sarcomere. Force-mapping revealed distinct transversal stiffness patterns for Z-/I-/M- and A-bands. A-band transversal stiffness was ~10x higher in rigor than in relaxed sarcomeres. Titin digestion by low-dose trypsin decreased rigor but not relaxed stiffness. A-band lateral stiffness did not differ between relaxed psoas and diaphragm sarcomeres at slack length (~2.2µm) but increased significantly after stretch to ~3.2µm and more highly in psoas than in diaphragm. Following osmotic compression by 5% dextran, A-band lateral stiffness rose 5-fold in both myofibril types. We conclude that stiff titin contributes more to transversal stiffness than compliant titin, confirming a role for titin in lateral force generation. In myocytes, osmotic forces may laterally compress the sarcomeric lattice to a degree that the titin contribution becomes negligible.