This paper develops models of the demand for and supply of elective (non-emergency) surgery using a panel of quarterly data for 200 English hospitals over the period 1995-2002. Unusually, distinct measures of supply (outpatients seen and inpatient admissions) and demand (outpatient referrals and decisions to admit) are available for each observation. These offer the opportunity to estimate separate empirical models of supply and demand using ordinary least squares (OLS) regression methods. However, the strong correlation between the residuals of these models suggests some merit in the deployment of seemingly unrelated regression (SUR) methods. Although both static and dynamic SUR estimations leave the results largely qualitatively unchanged, SUR estimation can have a considerable quantitative effect relative to the OLS results. For example, SUR estimation generates a lower elasticity of inpatient demand with respect to waiting time than that obtained via OLS. The results offer an important justification for more careful econometric modelling of hospital behaviour than has traditionally been employed in the health economics literature.