4Auditory steady-state responses (ASSRs) are auditory evoked potentials that reflect phase-locked neural activity to periodic stimuli. ASSRs are often evoked by tones with a modulated envelope, with sinusoidal envelopes being most common. However, it is unclear if and how the shape of the envelope affects ASSR responses. In this study, we used various trapezoidal modulated tones to evoke ASSRs (modulation frequency = 40 Hz) and studied the effect of four envelope parameters: attack time, hold time, decay time and off time. ASSR measurements in 20 normal hearing subjects showed that envelope shape significantly influenced responses: increased off time and/or increased decay time led to responses with a larger signal-to-noise-ratio (SNR). Response phase delay was significantly influenced by attack time and to a lesser degree by off time. We also simulated neural population responses that approximate ASSRs with a model of the auditory periphery (Bruce et al. 2018). The modulation depth of the simulated responses, i.e. the difference between maximum and minimum firing rate, correlated highly with the response SNRs found in the ASSR measurements. Longer decay time and off time enhanced the modulation depth both by decreasing the minimum firing rate and by increasing the maximum firing rate. In conclusion, custom envelopes with long decay and off time provide larger response SNRs and the benefit over the commonly used sinusoidal envelope was in the range of several dB.