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Abstract In this paper, we study the largest eigenvalues of sample covariance matrices with elliptically distributed data. We consider the sample covariance matrix $$Q=YY^{*},$$ where the data matrix $$Y \in \mathbb{R}^{p \times n}$$ contains i.i.d. $$p$$-dimensional observations $$\textbf{y}_{i}=\xi _{i}T\textbf{u}_{i},\;i=1,\dots ,n.$$ Here $$\textbf{u}_{i}$$ is distributed on the unit sphere, $$\xi _{i} \sim \xi $$ is some random variable that is independent of $$\textbf{u}_{i}$$ and $$T^{*}T=\varSigma $$ is some deterministic positive definite matrix. Under some mild regularity assumptions on $$\varSigma ,$$ assuming $$\xi ^{2}$$ has bounded support and certain decay behaviour near its edge so that the limiting spectral distribution of $$Q$$ has a square root decay behaviour near the spectral edge, we prove that the Tracy–Widom law holds for the largest eigenvalues of $$Q$$ when $$p$$ and $$n$$ are comparably large. Based on our results, we further construct some useful statistics to detect the signals when they are corrupted by high dimensional elliptically distributed noise.