An expanding cylindrical laminar flame kernel affected by random external strain rates and diffusivity is numerically simulated in order to gain insight into the influence of small-scale turbulence on the combustion variability in engines. In the simulations, the kernel is strained, as a whole, by external velocity gradients randomly generated with either Gaussian or log-normal probability density functions. The influence of small-scale turbulent heat and mass transfer is modeled by turbulent diffusivity, the randomness of which is controlled by the fluctuations in the viscous dissipation averaged over the kernel volume. The computed results show that small-scale phenomena can substantially affect the quenching characteristics of a small flame kernel and the kernel growth history rj(t); the scatter of the computed curves of rf(t) being mainly controlled by the scatter of the duration of the initial stage of kernel development. The results reveal the importance of small-scale turbulent straining for cyclic variability in spark ignition engines.