Foreign language anxiety (FLA), whose impact is often negative on learners' cognitive processing, happens when a learner pursues a foreign language as a non-native speaker. This study aimed to investigate anxiety in learning English as a foreign language and its influence on learners' cognitive processes. The sample comprised graduate and undergraduate students of RUDN university (n=306 respondents), who were asked to fill up an adapted Foreign Language Classroom Anxiety Scale. The data was analyzed through SPSS v.20 and descriptive statistics were drawn. The findings indicate a statistically important anxiety influence on language performance among university students in classroom settings. Interestingly, the findings also confirmed that foreign language anxiety negatively affects cognitive processing in learning the English language. The study also identified some important affective factors with regard to English language classrooms. These findings would provide useful insights in the domain of foreign language anxiety while taking cognitive dimensions of students' classroom environments. The study also contributes to language education, teaching and learning of English as foreign language, educational psychology, and cognitive sciences. The study recommends to provide more exposure to the learners about the target language to reduce anxiety. Future studies should consider socio-biographical variables such as gender, socioeconomic status, educational background, and age differences as significant variables for a more comprehensive analysis of foreign language anxiety.