A design mode, in which a casing is filled with a charge initiated off-centre (eccentric point initiation), is common in the field of explosion and structural protection. The fragment velocity distribution along the circumference of the casing is distinctly non-uniform due to the difference in blast loading around the circumference of the casing. To quantify the fragment velocity distribution, two kinds of cylindrical rings with different structural parameters were adopted. Static explosive experiments with three eccentric coefficients (0, 0.5, 1.0) were conducted with pulsed X-ray diagnostics. Using coefficients derived from experimental data and calculating the effects of both the eccentricity of initiation and angle around the circumference, an angle-dependent ratio of charge mass to casing mass has been derived as a mean to modify the fragment velocity formula of Gurney for this application. The derived formula was shown to correctly predict the fragment velocity distribution around the circumference of the cylindrical ring. The calculated velocity distributions show good agreement with the experimental results.