The elastic and hyperelastic properties of biological soft tissues have been of interest to the medical community as there are several applications where parameters characterizing these properties are critical for a reliable outcome. This includes applications such as surgery planning, needle biopsy and cancer diagnosis using medical imaging. While there has been considerable research on the measurement of the linear elastic modulus of small tissue samples, little research has been conducted for measuring parameters that characterize nonlinear elasticity of tissues included in slice specimens. In this paper, we present a method of measuring the hyperelastic parameters of tissue slice samples with tumours. In this method, to measure the hyperelastic properties of a tumour within a slice sample, the tumour was indented to acquire its force-displacement response while the slice remained intact. To calculate the hyperelastic parameters from the acquired data, we developed two inversion techniques that use the slice nonlinear finite element model as their forward problem solver. One of these techniques was based on nonlinear optimization while the other is a novel iterative technique that processes the variable slopes of the force-displacement response to calculate the hyperelastic parameters. The latter was developed specifically for the Yeoh and the second-order polynomial hyperelastic models, since we found that the other optimization-based inversion technique did not perform well with these models. To validate the proposed techniques, we performed numerical and phantom experiments. While we were able to achieve convergence with wide ranges of parameters of initial guesses to within 1% error with the numerical simulation experiments, we achieved convergence to within errors of around 5% with the tissue mimicking phantoms. Moreover, we successfully applied these techniques to data we acquired from nine pathological breast tissue slice specimens where the goal was to determine the hyperelastic properties of the tumour within the breast tissue slices.