A study is made of the external flow of an atmospheric-pressure burner-stabilised methane-oxygen-argon flame near an axisymmetric conical sampling probe with an orifice at the centre of the cone tip. The flow is simulated by solving the full set of unsteady Navier-Stokes equations using a recently developed original algorithm. Heat release due to chemical reactions is approximately described by a source term in the energy equation which provides a given temperature distribution in the unperturbed isobaric flame. On the probe orifice surface, the axial gas velocity is assumed to be equal to the local velocity of sound. A qualitative understanding of the nature and magnitude of the perturbing effects of the probe on the flame is obtained by comparing the steady flow near the probe and the unperturbed flame. Probe-induced distortions in the flame mixture composition are simulated by calculating concentration distributions of some species (CH4, CO2, H2O, and O2) in the flow field from the diffusion equation for binary gas mixtures (CH4 - Ar, CO2 - Ar, etc.) in a linear formulation. The effect of chemical reactions is approximately described by a source term in the diffusion equation which provides given concentration distributions in the unperturbed flame. The developed approach based on spatially fixed sources of energy and species concentrations provides more realistic simulations of probe-induced perturbations of the flame structure than the approaches described in the literature. The data demonstrating the nature of the probe-perturbed flame under conditions close to real ones were obtained for the first time.