A central composition design was developed to study the influence of process variables (temperature, pulping time, sulphite concentration, anthraquinone concentration and liquid/solid relation) on the properties of pulps (yield, holocellulose, α-cellulose and lignin contents, and brightness) and the paper sheets (stretch, burst index and tear index) obtained from them, in the sulphite pulping of olive tree wood. Equations that reproduce the properties of pulps prepared by sulphite pulping and of paper sheets obtained from it are reported. The proposed equations fit the experimental yield and the holocellulose and α-cellulose contents of the pulps with errors less than 5%, as well as brightness with errors less than 10%. Also, they reproduce the lignin content of the pulps, and the stretch, burst index and tear index of the paper sheets with errors less than 15%. Obtaining pulps with acceptably high yield, holocellulose and α-cellulose contents, and also a high brightness, in addition to low lignin contents, entails operating at a temperature of 193 °C for 143 min, using a sulphite concentration of 19.85%, an anthraquinone concentration of 0.1% and a liquid/solid relation of 6.24. These are also the most suitable conditions for obtaining paper sheets with a high stretch, burst index and tear index.