We present one of the very first extensive classifications of a large sample of molecular clouds based on their morphology. This is achieved using a recently published catalogue of 10 663 clouds obtained from the first data release of the Structure, Excitation and Dynamics of the Inner Galactic InterStellar Medium (SEDIGISM) survey. The clouds are classified into four different morphologies via visual inspection and using an automated algorithm - J plots. The visual inspection also serves as a test for the J plots algorithm as this is the first time it has been used on molecular gas. Generally, it has been found that the structure of molecular clouds is highly filamentary, and our observations indeed verify that most of our molecular clouds are elongated structures. Based on our visual classification of the 10 663 SEDIGISM clouds, 15% are ring-like, 57% are elongated, 15% are concentrated, and 10% are clumpy clouds. The remaining clouds do not belong to any of these morphology classes and are termed unclassified. We compare the SEDIGISM molecular clouds with structures identified through other surveys: the elongated structures from the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL) and the bubbles from Milky Way Project (MWP). We find that many of the ATLASGAL and MWP structures are velocity coherent. Elongated ATLASGAL structures overlap with ≈21% of the elongated SEDIGISM structures (elongated and clumpy clouds), and MWP bubbles overlap with ≈25% of the ring-like SEDIGISM clouds. We also analyse the star formation associated with different cloud morphologies using two different techniques. The first technique examines star formation efficiency and the dense gas fraction based on SEDIGISM cloud and ATLASGAL clump data. The second technique uses the highmass star formation threshold for molecular clouds. The results indicate that clouds with ring-like and clumpy morphologies show a higher degree of star formation. <P />Tables A.1-A.4 are only available at the CDS via anonymous ftp to <A href="http://cdsarc.u-strasbg.fr">cdsarc.u-strasbg.fr</A> (ftp://130.79.128.5) or via <A href="http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/663/A56">http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/663/A56</A>< Réduire