Method of utilizing process gas containing sulphur dioxide obtained from discontinuous processes, in the manufacture of sulphuric acid in a contact plant. When practicing the method according to the invention, all of the process gas, or a predetermined amount thereof, is withdrawn from the process during process operational periods, in which gas containing sulphur dioxide is generated, and the sulphur dioxide contained by the withdrawn gas is at least partially separated therefrom to form a liquid phase containing the amount of sulphur dioxide separated. The gas partially freed from sulphur dioxide, together with any non-withdrawn process gas, is passed to the contact plant for manufacturing sulphuric acid. Stored absorption liquid is utilized during those periods in which no process gases are produced or passed to the contact plant or in which the process gases contain insufficient sulphur dioxide. Sulphur dioxide is stripped from the liquid phase with the aid of a carrier gas, and the carrier gas, together with the stripped sulphur dioxide, is passed to the contact plant. This enables a required amount of gas and sulphur dioxide to be constantly supplied to the contact plant, even during those periods when the discontinuous process does not produce a sulphur-dioxide-containing gas or produce a gas having an insufficiently high sulphur-dioxide amount.