A large number of parameters such as material properties, geometry, and structural strength are involved in the design and analysis of cemented hip implants. Uncertainties in these parameters have a potential to compromise the structural performance and lifetime of implants. Statistical analyses are well suited to investigating this type of problem as they can estimate the influence of these uncertainties on the incidence of failure. Recent investigations have focused on the effect of uncertainty in cement properties and loading condition on the integrity of the construct. The present study hypothesizes that geometrical uncertainties will play a role in cement mantle failure. Finite element input parameters were simulated as random variables and different modes of failure were investigated using a response surface method (RSM). The magnitude of random von Mises stresses varied up to 8 MPa, compared with a maximum nominal value of 2.38 MPa. Results obtained using RSM are shown to match well with a benchmark direct Monte Carlo simulation method. The resulting probability that the maximum cement stress will exceed the nominal stress is 62%. The load and the bone and prosthesis geometries were found to be the parameters most likely to influence the magnitude of the cement stresses and therefore to contribute most to the probability of failure.