Variations of critical temperature $T_c$ and in-plane critical field $H_{c2}$ of $text{Sr}_2text{Ru}text{O}_4$ under uniaxial stress have recently been reported. We compare the strain dependence of $T_c$ and $H_{c2}$ in various pairing channels ($d$-wave, extended s-wave and $p$-wave) with the experimental observations, by studying a three-band tight-binding model that includes effects of spin-orbit and Zeeman couplings and a separable pairing interaction. Our study helps narrow down the possibility of pairing channels. The importance of the multi-band nature of $text{Sr}_2text{Ru}text{O}_4$ is also highlighted.
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