The main topic of the paper is to present a new numerical technique for simulating gas-solid reactions. The modelling of gas-sided reactions has been investigated for the last three decades very intensely. There is a number of models and methods to solve them. The authors consider gas-solid reactions that include both internal reaction and reaction on the shrinking core surface. This model was derived by \textit{S. K. Bhatia} [Perturbation analysis of gas-solid reactions: I. Solid of low initial permeability. Chem. Engng. Sci. 46, 173-182 (1991)]. Some transformations are introduced and this model can be reduced to dimensionless form which includes a self-adjoint, two-point boundary-value problem for the concentration of the gas reaction. At the same time these transformations produce two initial-value problems for the conversion of solid reactant and the interface position. Having arrived at this point they use a technique which involves the Petrov-Galerkin method with spline test functions and piecewise linear test functions. For the two initial-value problems they use predictor-corrector methods. In Section 2, they follow the model of Bhatia with some extra assumptions. Under these conditions they write the reaction-diffusion equations: \[ {\partial(\varepsilon G^*)\over\partial t^*}= {1\over r^{*2}} {\partial\over\partial r^*} \Biggl[D^*_1(S^*) r^{*2}{\partial G^*\over\partial r^*}\Biggr]- k^*G^*f(S^*), \rho_B(1-\varepsilon_0){\partial S^*\over\partial t^*}= bk^*G^* f(S^*), \] where \(G^*\) is the concentration of the gas reactant in the internal region, \(f(S^*)\) is a function describing the change in reaction rate with conversion, \(S^*\) is the local conversion of solid reactant, \(\varepsilon\) is a porosity (\(\varepsilon_0\)-initial porosity), \(\rho_B\) is a molar density of solid reactant. The above equations are supported by the transport equation for the outer region and the solid reactant balance equation at the surface of the shrinking care. After some calculation at the end of this section they obtain a dimensionless form that is a subject of their study. In Section 3, a weak form of the above equations is introduced. This weak form is discretized by means of Petrov-Galerkin finite element technique. Two types of test functions are used (\(\overline L\)-splines and standard piecewise-linear hat functions). This leads to a linear equation of the form \(Au=f\), where \(A\) is a tridiagonal matrix. In Sections 4 and 5, some numerical simulations and results are presented. Especially the behaviour of their model when some parameters go to limits is discussed. It should be stressed that there is no limit to the range of the parameters. The paper is written very clearly and with paying attention to details and good use of symbols.