Tumour cell invasion is crucial for cancer metastasis, which is the main cause of cancer mortality. An important group of proteins involved in cancer invasion are the Heat Shock Proteins (HSPs). According to experimental data, inhibition of one of these proteins, Hsp90, slows down cancer cells while they are invading tissue, but does not affect the synthesis of matrix metalloproteinases (MMP2 and MMP9), which are very important for cancer metastasis, acting as extracellular matrix (ECM) degrading enzymes. To test different biological hypotheses regarding how precisely Hsp90 influences tumour invasion, in this paper we use a model of solid tumour growth which accounts for the interactions between Hsp90 dynamics and the migration of cancer cells and, alternatively, between Hsp90 dynamics and the synthesis of matrix degrading enzymes (MDEs). The model consists of a system of reaction-diffusion-taxis partial differential equations describing interactions between cancer cells, MDE, and the host tissue (ECM). Using numerical simulations we investigate the effects of the administration of Hsp90 inhibitors on the dynamics of tumour invasion. Alternative mechanisms of reduction of cancer invasiveness result in different simulated patterns of the invading tumour cells. Therefore, predictions of the model suggest experiments which might be performed to develop a deeper understanding of the tumour invasion process.