A sequence of goals scored during sport match is modelled as a realization of two dependent random point processes. It is assumed that the scoring intensity of each team has several components depending on time or on factors describing the teams and other conditions of the match. This dependence is modelled with the aid of a semi-parametric multiplicative regression model of intensity. A method of model evaluation is presented and demonstrated on a real data set. Prediction obtained from the model via the Monte Carlo simulation is compared with real results.